Physics of Open Quantum Systems


 

Our starting point was the general Markovian quantum master equation, originally derived by Lindblad from axiomatic reasons (J.Math.Phys. 48 (1976) 119), which has been put into a physical form for a harmonic oscillator by Sandulescu and Scutaru (Ann.Phys. 173 (1987) 277).

 

Later, we applied this equation to some physical effects: atom-field interaction (A. Sandulescu, E. Stefanescu, Physica A 161 (1989) 525), cold fission (E. Stefanescu, W. Scheid, A. Sandulescu, and W. Greiner, Phys.Rev. C  53 (1976) 3014), and nuclear giant resonances (E. Stefanescu, RJ. Liotta, and A. Sandulescu, Phys.Rev. C 57 (1998) 798). Although this master equation is in agreement with the quantum principles, disadvantageously it has a number of unspecified parameters that do not enable an explicit description of the various dissipative processes.

 

Consequently, our further studies have been devoted to the description of the more realistic system of a fermions assembly in a dissipative environment of other fermions (E. Stefanescu, A. Sandulescu, and W. Scheid, Int.J.Mod.Phys. E 9 (2000) 17, E. Stefanescu, A. Sandulescu, Int.J.Mod.Phys. E 11 (2002) 119), bosons, and free electromagnetic field (E. Stefanescu, A. Sandulescu, Int.J.Mod.Phys. E 11 (2002) 379). Thus, we obtained a Markovian master equation with analytical coefficients depending on microscopic quantities: two-body potentials between the system and the environment particles, densities of the environment states, occupation probabilities of these states, and, implicitly, temperature.

 

Afterwards (E. Stefanescu, Physica A 350 (2005) 227) we showed that this equation is in agreement with the detailed balance principle and provides plausible results in some application fields as super radiance, dynamics of a harmonic oscillator in free electromagnetic field, electron decay in a semiconductor quantum dot coupled with a conduction region.

 

Recently (E. Stefanescu, W. Scheid, Physica A 374 (2007) 203), we proposed a semiconductor device for converting the heat of the environment into coherent electromagnetic energy. Generally, we believe that this description of a dissipative quantum system could lead to very important applications in nanotechnology.

At present, our efforts are dedicated to the non-Markovian dynamics of a system of fermions interacting with a coherent electromagnetic field and to the conversion of the environmental heat into usable energy.  

 

  1. E. Stefanescu, The Relativistic Dynamics as a Quantum Effect, Journal of Basic and Applied Research International 1(1): 13-23, 2014

Abstract

In this paper we develop a Unitary Quantum Relativistic Theory. We show that the wavy nature of a quantum particle involves the relativistic dynamics of the wave-packet of this particle, and a field of interaction described by Lorentz’s force and three of the four Maxwell equations: the electromagnetic induction law, and the flow laws of the electric and magnetic fields. These equations arise from the group velocity, which is of the form of the Lagrange equation, and from a relativistic principle for wave functions, which asserts that in any system of reference a wave-function has a bounded spectrum with a velocity limit c. When a magnetic circuit law is considered for a field interacting with a quantum particle, this is an electromagnetic field, propagating with the velocity c.

 

  1. E. Stefanescu, Open Quantum Physics and Environmental Heat Conversion into, Bentham Science Publishers, Sharjah (UAE), Brussels, Danvers (Massachusetts, USA)

Abstract

1. Introduction, Pp. 1-4 (4) 
Abstract 
This eBook is devoted to the domain of physics we call Open Quantum Physics, which seemed important for the new field of research of the
environmental heat conversion into usable energy. For this research, a special mathematical tool has been used, consisting of master equations for systems of particles as Fermions, Bosons, and electromagnetic field. This effort was based on the previous results of Lindblad, Sandulescu, and Scutaru for a description of the dissipative coupling of a system of interest in accordance with the quantum principles. We used the method of Ford, Lewis, and O’Connell for reducing the total dynamics to a master equation for a system of interest. The results of our research are presented in this eBook in a more general framework of open physics. 
2. Quantum dynamics, Pp. 5-52 (48) 
Abstract 
In this chapter, we derived some elements of quantum mechanics, which are essential for the further development of our theory: the momentum of a system of Fermions in the second quantization, the coordinate and momentum of a harmonic oscillator as a unique operator at two different moments of time, Boson and Fermion operator algebra, coherent states, the electron-field interaction, the quantization of the electromagnetic field, Boson and Fermion distributions, and densities of states in a degenerate, or a non-degenerate system of Fermions. Our starting point is the wave nature of a quantum particle, the Hamiltonian equations were obtained as group velocities in the two conjugate spaces of the wave, of the coordinates and of the momentum. In this way, the Schr¨odinger equation and the electron-field potential of interaction are obtained from quantum equations generated by the particle wave function. 
3. Dissipative dynamics, Pp. 53-92 (40) 
Abstract 
In this chapter, we describe various mechanisms and characteristics of dissipation, mostly in physical terms, as they have been perceived at the beginning. We get a microscopic understanding of temperature, and of the main dissipation effects. We obtain the entropy dynamics, according to principle two of thermodynamics, from the Pauli master equation, as the simplest description of a system defined by states, occupation probabilities, and transition probabilities. For various expansions of these probabilities as functions of coordinates, stochastic equations are obtained for the time evolutions of these coordinates. In this framework, we describe the electron and hole transport in semiconductors. We present various trials for completing a Schr¨odinger equation with dissipative terms, and the method of projection operators for a description of a system coupled to a dissipative environment. 
4. Axiomatic open quantum physics, Pp. 93-108 (16) 
Abstract 
This chapter is devoted to Lindblad master equation, obtained by a generalization of the quantum dynamic group to a time dependent semigroup. For this equation, we present a demonstration of Alicki and Lendi, obtained by a linear approximation of the openness operator, which describes the time evolution of a system of interest in an environment. We re-obtain this equation by taking the total dynamic equation with a bilinear dissipative potential in system and environment operators, and tracing over the environment states. In this way, we get physical expressions of the dissipation coefficients, as functions of the system operators. We present the quantum theory of Sandulescu and Scutaru, where the dissipative dynamics is described by friction and diffusion processes, with coefficients which satisfy fundamental constraints. 
5. Quantum tunneling with dissipative coupling, Pp. 109-126 (18) 
Abstract 
This chapter is devoted to quantum tunneling, as a basic quantum process, essential for important applications. Tunneling between two wells, of the double well potential of a one particle system of interest, makes sense only when a second system, capable to distinguish between the presence of the particle in a well, or in the other well, is present. The potential of interaction between such two systems is called tunneling operator. We treat a few problems of interest as tunneling in a quasi-continuum of states, the energy shift in a well by the proximity of another well, dissipation effects, and tunneling spectrum. 
6. Atom-field interaction with dissipative coupling, Pp. 127-154 (28) 
Abstract 
In this chapter, we treat the basic quantum process of electromagnetic field propagation through an atomic system in a resonant Fabry-Perot cavity. We obtain the transmission characteristic of such a cavity, which is a basic element for a quantum heat converter. When the system is opened only by a population decay and a polarization dephasing, we get only an optical bistability characteristic. By openness according to the Lindblad- Sandulescu-Scutaru theory, we get also a coupling through environment between population and polarization, which, in some conditions, leads to an energy transfer from the disordered environment to the coherent electromagnetic field. We find that this phenomenon, which has experimental evidence, is an effect of an atom-atom coupling. 

7. Microscopic open quantum physics, Pp. 155-190 (36) 
Abstract 
In this chapter, we derive quantum master equations with explicit, microscopic coefficients, for the systems of interest of a superradiant semiconductor structure: the active electrons, the electromagnetic field, and the optical crystal vibrations. These vibrations determine an important retardation in the field propagation (refractive index), and a spectrum splitting (the Raman effect). For the active electrons we consider three environmental systems: the quasi-free electrons/holes of the conduction regions, the crystal lattice vibrations excited by electron transitions, and the free electromagnetic field. For the electromagnetic field, we consider the absorption by coupling to the conduction electrons/holes, and to the optical vibrations of the crystal, while these vibrations are damped by coupling with the valence electron transitions to thermally released states. For the electron-field coupling we consider the potential derived in chapter 2 from the Lorentz force, while the momentum difference is supposed to be taken by the crystal lattce. For the coupling of the crystal vibrations to the electromagnetic field and electron transitions we consider potentials obtained from the momentum conservation. For the active electrons, we find a quantum master equation with a Markovian term describing correlated transitions with the environmental particles, and a non-Markovian term given by the self-consistent field of the environmental particles. Since the dissipative environment of the electromagnetic field is contained inside the quantization volume of this field, which is taken as a unit volume, its quantum master equation includes a dissipative term of a space integral form. For the field mean values, the dissipation integral, of propagation through the dissipative environment, can be divided in two parts: an integral from the initial coordinate up to the boundary of the quantum uncertainty region, taken for a coherent wave, which describes dephasing, and an integral over the uncertainty region, which describes absorption. Similar equations are obtained for the optical vibration field. When the vibrational field is eliminated from these equations, we obtain a frequency splitting, corresponding to the Raman effect, and an absorption rate, including the absorption of the electromagnetic waves by conduction electrons/holes, and the absorption of the vibrational waves by the valence electrons, excited by the crystal deformations in the thermally released states. 
8. Open hydrogen atom, Pp. 191-208 (18) 
Abstract 
In this chapter, we apply our quantum master equation for a system of Fermions in free electromagnetic field to a hydrogen atom. We obtain a quantum master equation describing transitions between the eigenstates of a hydrogen atom, with coefficients depending on the hydrogen wave functions. We find that these coefficients are in agreement with published experimental data for life times of the lower excited states. 
9. Quantum heat converter, Pp. 209-230 (22) 
Abstract 
In this chapter, we apply the theory developed in chapter 7 to a superradiant semiconductor device for the conversion of the environmental heat into coherent electromagnetic energy. The operation principle of the device is formulated in simple terms, as a superradiant flow mainly supplied by heat absorption, only a much smaller part of the energy necessary for producing this flow being supplied from outside. This mechanism seems to counter the second principle of thermodynamics, but in fact does not, because this principle refers to an atomic system, describable by the Pauli master equation, as we showed in subsection 3.2.1. Any modification of this equation, as is our case of interaction with an electromagnetic field, involves a modification of the entropy dynamics. We calculate the wave-function, the corresponding dipole moments, and the dissipation coefficients, and obtain the superradiant power in the mean field approximation. When the field propagation, coupled to the crystal optical vibration, is taken into account, we get a resonance frequency shift with the Raman frequency, and a small decrease of the superradiant power by Raman effect. 

 

  1. E. Stefanescu, Open Quantum Systems of Particles and Principle 2 of Thermodynamics, Int. Summer School "Dynamics of open nuclear systems", July 9-20, 2012, Predeal, Romania.

Abstract

 

We consider quantum master equations for a system of Fermions and an electromagnetic field, and apply these equations to a superradiant semiconductor structure converting environmental heat into coherent electromagnetic energy. For a non-irradiative system, these equations describe a time evolution with entropy increase, according to principle 2 of thermodynamics. However, for a superradiant system, the entropy may decrease, while the asymptotic solution of these equations, corresponding to constant entropy, describes a field radiation on the account of environmental heat absorption by Peltier effect.

 
  1. Eliade Stefanescu, Master equation and conversion of environmental heat into coherent electromagnetic energy, J. Prog. Quantum Electron. 34 (2010) 349–408, doi: 10.1016/j.pquantelec.2010.06.003.

Abstract

 

We derive a non-Markovian master equation for the long-time dynamics of a system of Fermions interacting with a coherent electromagnetic field, in an environment of other Fermions, Bosons, and free electromagnetic field. This equation is applied to a superradiant p–i–n semiconductor heterostructure with quantum dots in a Fabry–Perot cavity, we recently proposed for converting environmental heat into coherent electromagnetic energy. While a current is injected in the device, a superradiant field is generated by quantum transitions in quantum dots, through the very thin i-layers. Dissipation is described by correlated transitions of the system and environment particles, transitions of the system particles induced by the thermal fluctuations of the self-consistent field of the environment particles, and non-local in time effects of these fluctuations. We show that, for a finite spectrum of states and a sufficiently weak dissipative coupling, this equation preserves the positivity of the density matrix during the whole evolution of the system. The preservation of the positivity is also guaranteed in the rotating-wave approximation. For a rather short fluctuation time on the scale of the system dynamics, these fluctuations tend to wash out the non-Markovian integral in a long-time evolution, this integral remaining significant only during a rather short memory time. We derive explicit expressions of the superradiant power for two possible configurations of the superradiant device: (1) a longitudinal device, with the superradiant mode propagating in the direction of the injected current, i.e. perpendicularly to the semiconductor structure, and (2) a transversal device, with the superradiant mode propagating perpendicularly to the injected current, i.e. in the plane of the semiconductor structure. The active electrons, tunneling through the i-zone between the two quantum dot arrays, are coupled to a coherent superradiant mode, and to a dissipative environment including four components, namely: (1) the quasi-free electrons of the conduction n-region, (2) the quasi-free holes of the conduction p-region, (3) the vibrations of the crystal lattice, and (4) the free electromagnetic field. To diminish the coupling of the active electrons to the quasi-free conduction electrons and holes, the quantum dot arrays are separated from the two n and p conduction regions by potential barriers, which bound the two-well potential corresponding to these arrays. We obtain analytical expressions of the dissipation coefficients, which include simple dependences on the parameters of the semiconductor device, and are transparent to physical interpretations. We describe the dynamics of the system by non-Markovian optical equations with additional terms for the current injection, the radiation of the field, and the dissipative processes. We study the dependence of the dissipative coefficients on the physical parameters of the system, and the operation performances as functions of these parameters. We show that the decay rate of the superradiant electrons due to the coupling to the conduction electrons and holes is lower than the decay rate due to the coupling to the crystal vibrations, while the decay due to the coupling to the free electromagnetic field is quite negligible. According to the non-Markovian term arising in the optical equations, the system dynamics is significantly influenced by the thermal fluctuations of the self- consistent field of the quasi-free electrons and holes in the conduction regions n and p, respectively. We study the dependence of the superradiant power on the injected current, and the effects of the non-Markovian fluctuations. In comparison with a longitudinal device, a transversal device has a lower increase of the superradiant power with the injected current, but also a lower threshold current and a lesser sensitivity to thermal fluctuations.

 

  1. OPEN QUANTUM PHYSICS AND ENVIRONMENTAL HEAT CONVERSION INTO USABLE ENERGY, in progress.
  2. LONGITUDINAL QUANTUM HEAT CONVERTER, Inventors: Eliade Stefanescu and Lucien Eugene Cornescu, Patent US 20090007950 (US Patent Office, Jan. 08 2009), http://www.faqs.org/patents/app/20090007950.

Abstract

 

A method for the environment heat conversion in coherent electromagnetic energy by a superradiant quantum decay and a thermal excitation of a system of electrons is disclosed. A semiconductor device is also disclosed comprising a system of n-i-p-n transistors, a double array of quantum dots on the two sides of the thin i-layer of the n-i emitter, a system of intermediate n and p layers separating the active quantum region from the n and respectively p regions by potential barriers, a metal front electrode, a heat absorber in intimate contact with this electrode, a semitransparent rear electrode forming with the front electrode a Fabry-Perot resonator tuned with the electron quantum transition frequency through the i-layer, and an output semitransparent mirror of the same transparency as the transparency of the rear electrode, by this forming with the rear electrode a total transmission Fabry-Perot resonator.

 

  1. TRANSVERSAL QUANTUM HEAT CONVERTER, Inventors: Eliade Stefanescu and Lucien Eugene Cornescu, Patent US 20100019618 (US Patent Office, Jan. 28 2010), http://www.faqs.org/patents/app/20100019618.

Abstract

 

A semiconductor device for the environment heat conversion in coherent electromagnetic energy by a super radiant quantum decay and a thermal excitation of a system of electrons in a super lattice of n-i-p-n transistors with quantum dots on the two sides of the i-layer, and potential barriers for separating the quantum transition n-i-p regions from the adjacent conduction n and p regions. When an electron current is injected in a perpendicular direction on the transistor arrays, a super radiant field is generated in the plane of these arrays, with a power mainly obtained by a heat absorption that is much larger than the absorbed electric power. The device also includes an input heat absorber, and an output Fabry-Perot resonator with total transmission for the electromagnetic energy extraction from the device active region.

 

  1. QUANTUM INJECTION SYSTEM, Inventors: Eliade Stefanescu and Lucien Eugene Cornescu, Patent US 20090007951 (US Patent Office, Jan. 08 2009), http://www.faqs.org/patents/app/20090007951.

Abstract

 

A system is disclosed comprising a package of active Fabry-Perot transmitters and an electric charge accumulator for converting a part of coherent electromagnetic power in electric power at the proper voltage of this accumulator. An active Fabry-Perot transmitter is a semiconductor device comprising a packet of p-i-n diodes with double quantum dots on the two sides of the i-layer, separated by potential barriers from the conduction regions. The semiconductor structure is placed in a Fabry-Perot cavity with total transmission. While a resonant coherent electromagnetic beam is crossing the Fabry-Perot cavity, a small part from the electromagnetic energy is captured by resonant electron excitations through the i-layer, injecting an electron current in the device.

 

  1. Eliade Stefanescu, Dissipative systems (in Romanian), The Printing House of the Romanian Academy (Bucharest 2000). 
  2. Eliade Stefanescu, Werner Scheid, and Aurel Sandulescu, Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field, Annals of Physics, 323 (2008) 1168-1190. 

Abstract

 

For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad's form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode crossing an array of two-level quantum dots.

 

  1. Eliade Stefanescu and Werner Scheid, Superradiant dissipative tunneling in a double p-i-n semiconductor heterostructure with thermal injection of electrons, Physica A 374 (2007) 2003. 

 Abstract

We propose a semiconductor device with two p-i-n junctions maintained at two different temperatures. When the current injected in the device due to this temperature difference exceeds a threshold value, a superradiant field is created in the first gate that induces an additional current in the second gate. The injection current is amplified by this reaction loop. In this way, the heat flow between the two junctions is partially transformed into superradiant power.

 

  1. Eliade Stefanescu, Dynamics of a Fermi system with resonant dissipation and dynamical detailed balance, Physica A 350 (2005) 227. 

 Abstract

The dissipative dynamics of a system of Fermions is described in the framework of a resonance model - the quantum master equation describes two-body correlations of the system with the environment particles. This equation, with microscopic coefficients depending on the exactly known two-body potential between the system and the environment particles, is discussed in comparison with other master equations, obtained on axiomatic grounds, or derived from a coupling with an environment of harmonic oscillators without altering the quantum conditions. The asymptotic solution is in accordance with the detailed balance principle, and with other generally accepted conditions satisfied during the whole time-evolution: Pauli master equations for the diagonal elements of the density matrix, and damped Bloch-Feynman equations for the non-diagonal ones, that we call dynamical detailed balance. For a harmonic oscillator coupled with the electromagnetic field through dipole interaction, a master equation with transition operators between successive levels is obtained. As an application, the decay width of a quantum logic gate is calculated.

 

  1. Eliade Stefanescu and Aurel Sandulescu, Dynamics of a Fermi system in a blackbody radiation field, Int.J.Mod Phys. E 11 (2002) 379. 

Abstract

 

We derive a quantum master equation for a system of Fermions coupled to the blackbody radiation field through the electric-dipole interaction. This equation is of Lindblad’s form, with a Hamiltonian part of the shell-model, and a dissipative part with microscopic coefficients, depending on physical constants, matrix elements, and parametrically only on temperature.

 

  1. Eliade Stefanescu and Aurel Sandulescu, Microscopic coefficients for the quantum master equation of a Fermi system, Int.J.Mod.Phys. E 11 (2002) 119. 

Abstract

 

In a previous paper, we derived a master equation for Fermions, of Lindblad’s form, with coefficients depending on microscopic quantities. In this paper, we study the properties of the dissipative coefficients taking into account the explicit expressions of: (a) the matrix elements of the dissipative potential, evaluated from the condition that, essentially, this potential induces transitions among the system eigenstates without significantly modifying these states, (b) the densities of the environment states according to the Thomas-Fermi model, and (c) the occupation probabilities of these states taken as a Fermi-Dirac distribution. The matrix of these coefficients correctly describes the system dynamics: for a normal, Fermi-Dirac distribution of the environment population, the decays dominate the excitation processes; (b) for an inverted (exotic) distribution of this population, specific to a clustering state, the excitation processes are dominant.

 

  1.  E. Stefanescu, A. Sandulescu, and W. Scheid, The collision decay of a Fermi system interacting with a many-mode electromagnetic field, Int.J.Mod.Phys. E 9 (2000) 17. 

Abstract

 

We consider a system of Z Fermions coupled to a dissipative environment through a two-body potential. We represent the system in a basis of single-particle, two-particle, … Z-particle excited states. Using a procedure for averaging the rapid oscillations of the reduced density matrix in the interaction picture, the master equation of the system takes the form of a series expansion of powers of the dissipative potential matrix elements. The term of the second-order describes single-particle transitions, while the higher-order terms correspond to correlated transitions of the system particles. For the second and the third-order terms, we derive microscopic expressions of the dissipative coefficients. For dissipative systems, when the system collectivity is broken into pieces through quantum diffusion, we use the quantum master equation of the second-order approximation. This equation satisfies basic physical conditions: particle conservation, Fermi-Dirac or Bose-Einstein distributions as asymptotic solutions of the populations and entropy increase. On this basis, the decay of a Fermi system interacting with a many-mode electromagnetic field is described in terms of microscopic quantities: the matrix elements of the dissipative potential, the densities of the environment states, and the occupation probabilities of these states. A near dipole-dipole interaction of the system with other neighboring systems is taken into account. In addition to the coupling of the polarization with the population, included in the usual equations for two-level systems as a non-linear detuning, in equations for N-level systems two new couplings appear: a coupling due to the proximity potential, and a coupling due to the local field corrections, as a renormalization of the Rabi frequencies.

 

  1.  E. Stefanescu, R. J. Liotta, and A. Sandulescu, Giant resonances as collective states with dissipative coupling, Phys.Rev. C 57 (1998) 798. 

Abstract

 

We describe giant resonances as the collective coordinates of a harmonic oscillator with dissipative coupling. Using a quantum master equation, the energy and width of the first two levels are obtained as functions of temperature and of the dissipative coupling strength. On this basis, we evaluate the ratio of the two spectral linewidths. The result agrees with available experimental data. We evaluate transition matrix elements among particle excitations belonging to the environment and find a weak dependence on temperature.

 

  1.  E. Stefanescu, W. Scheid, A. Sandulescu, and W. Greiner, Cold fission as cluster decay with dissipation, Phys.Rev. C 53 (1996) 3014.

Abstract

 

For cold (neutronless) fission we consider an analytical model of quantum tunneling with dissipation through a barrier U(q) evaluated with a M3Y nucleon-nucleon force. We calculate the tunneling spectrum, i.e. the fission rate as a function of the total kinetic energy of the fragments. The theoretical results are compared with the experimental data obtained for the fine structure of two cold fission modes of 252Cf: 148Ba+104Mo and 146Ba+106Mo. Taking into account the dissipative coupling of the potential function U(q) and of the momentum p with all the other neglected coordinates, we obtained a remarkable agreement with the experimental data. We conclude that the cold fission process is a spontaneous decay with a spectrum determined by the shape of the barrier and amplitude depending on the strength of the dissipative coupling.

 

  1.  E. Stefanescu and P. Sterian, Exact quantum master equations for Markoffian systems, Opt.Eng. 35 (1996) 1.

 Abstract

We show that the general quantum mater equation used in quantum optics can be put in the form of Lindblad’s master equation obtained in the frame of the general theory of dynamical semigroups. In this case, the dissipative interaction is described in the most general form by a system of openness parameters. We find the expressions of these parameters as functions of the operators of the dissipative environment.

 

  1.  E. Stefanescu, A. Sandulescu, and W. Greiner, Analytical model for quantum tunneling with dissipation through a fission-like barrier, J.Phys. G: Nucl.Part.Phys. 20 (1994) 811.

 Abstract

Analytical expressions for the spectral density of the tunneling rate are found for a fission-like analytical barrier having three parts: an internal part approximated by a harmonic oscillator, a top part considered constant, and an external part considered as a Coulomb potential. We found that environment-assisted tunneling processes are present for all three regions and that an environment-stimulated decay is significant only for the coulomb part of the barrier. Numerical calculations are made for the cold fission of 236U: 138Xe+98Sr.

 

  1.  A. Isar, A. Sandulescu, H. Scutaru, E. Stefanescu, and W. Scheid, Open quantum systems, Int.J.Mod.Phys. E 3 (1994) 635.

 Abstract

The damping of the harmonic oscillator is studied in the framework of the Lindblad theory of open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg, and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in literature are particular cases of the Lindblad equation and that not all of these equations are satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into Fokker-Planck equations for quasi-probability distributions and a comparative study is made for the Glauber P representation, the antinormal ordering Q representation, and the Wigner W representation. The density matrix is represented via a generating function, which is obtained by solving a time-dependent linear potential differential equation derived from the master equation. Illustrative examples for specific initial conditions of the density matrix are provided. The solution of the master equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding (for example) to a coherent wavefunction. The damped harmonic oscillator is applied for the description of the charge equilibration mode observed in deep inelastic reactions. For a system consisting of two harmonic oscillators the time-dependence of expectation values, Wigner function, and Weyl operator are obtained and discussed. In addition models for the damping of the angular momentum are studied. Using this theory to the quantum tunneling through the nuclear barrier, besides Gamow’s transitions with energy conservation, additional transitions with energy loss are found. The tunneling spectrum is obtained as a function of the barrier characteristics. When this theory is used to the resonant atom-field interaction, new optical equations describing the coupling through the environment of the atomic observables are obtained. With these equations, some characteristics of the laser radiation absorption spectrum and optical bistability are described.

 

  1.  E. Stefanescu, A. Sandulescu, and W. Greiner, Quantum tunneling in open systems, Int.J.Mod.Phys. E 2 (1993) 233.

 Abstract

We study the barrier penetrability in the frame of the Lindblad theory of open quantum systems. In addition to the diagonal elements of the density matrix, leading to Gamow’s formula, new terms, describing energy dissipation and spectral line broadening effects, are obtained. It is shown that the presence of a dissipative environment increases the barrier penetrability, in accordance with a very simple physical interpretation: for a system initially found in its ground state the dissipation can lead only to transitions to the reaction channels where lower energy levels exist.

 

  1.  A. Sandulescu and E. Stefanescu, New optical equations for the interaction of a two-level atom with a single mode of the electromagnetic field, Physica A 161 (1989) 525.

 Abstract

Based on the theory of open quantum systems, we derive new optical equations, more general than the conventional Bloch equations: new terms describing couplings of the observables through the environment and an asymmetry of the dephasing rates for the two polarization observables are obtained. We show that, due to the new coupling of the population with the polarization through the environment, negative values of the absorption coefficient are possible. We find experimental evidence of this new coupling by comparing the bistability characteristic obtained from the new equations, for a nonlinear Fabry-Perot resonator, with the experimental data of Sandle and Gallagher.