scholarly journals ASYMPTOTIC ENTANGLEMENT IN OPEN QUANTUM SYSTEMS

2008 ◽  
Vol 06 (supp01) ◽  
pp. 689-694 ◽  
Author(s):  
AURELIAN ISAR
Keyword(s):  
Open Systems ◽  
Open Quantum Systems ◽  
Continuous Variable ◽  
Harmonic Oscillators ◽  
Asymptotic State ◽  
Input State ◽  
Initial State ◽  
Bipartite State ◽  
Time Regime ◽  
Long Time

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.

scholarly journals Entanglement Generation and Evolution in Open Quantum Systems

2009 ◽  
Vol 16 (02n03) ◽  
pp. 205-219 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Time Evolution ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Continuous Variable ◽  
Harmonic Oscillators ◽  
Input State ◽  
Entanglement Generation ◽  
Gaussian States ◽  
Gaussian Input ◽  
Necessary And Sufficient

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we show that for certain values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.

scholarly journals Generation of Quantum Correlations in Bipartite Gaussian Open Quantum Systems

2018 ◽  
Vol 173 ◽  
pp. 01006 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Open Systems ◽  
Thermal Environment ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Thermal Bath ◽  
Initial State ◽  
Entanglement Generation ◽  
Strength Of Interaction ◽  
Zero Values

We describe the generation of quantum correlations (entanglement, discord and steering) in a system composed of two coupled non-resonant bosonic modes immersed in a common thermal reservoir, in the framework of the theory of open systems. We show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and strength of interaction between the two bosonic modes. We also show that for initial uni-modal squeezed states Gaussian discord can be generated for all non-zero values of the strength of interaction between the modes. Likewise, for an initial separable state, a generation of Gaussian steering may take place temporarily, for definite values of the parameters characterizing the initial state and the thermal environment, and the strength of coupling between the two modes.

Effects of static noise on the dynamics of quantum correlations for a system of three qubits

2017 ◽  
Vol 31 (08) ◽  
pp. 1750046 ◽  
Author(s):  
Tenemeza Kenfack Lionel ◽  
Tchoffo Martin ◽  
Fouokeng Georges Collince ◽  
Lukong Cornelius Fai
Keyword(s):  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Entangled State ◽  
Environment Interaction ◽  
Initial State ◽  
Text Type ◽  
System Environment ◽  
Entanglement Witnesses ◽  
Long Time ◽  
Static Noise

Correlations in open quantum systems exhibit peculiar phenomena under the effect of various sources of noise. Here, we investigate the dynamics of entanglement and quantum discord (QD) for three noninteracting qubits coupled with a classical environmental static noise characterized by an external random field. Two initial entangled states of the system are examined, namely, the GHZ- and [Formula: see text]-type states. The system-environment interaction is here analyzed in three different configurations, namely, independent, mixed and common environments. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the purity of the initial entangled state. Indeed, depending on the type of interaction and the value of the purity of the initial state, peculiar phenomena such as sudden death, revivals and long-time survival of quantum correlations are observed. On the other hand, our results clearly show that quantum correlations initially present in the [Formula: see text]-type states are less robust than those of the GHZ-type states. Furthermore, we find that the long-time survival of entanglement can be detected by means of the suitable entanglement witnesses.

Quantum Discord of Two Bosonic Modes in Two-Reservoir Model

2013 ◽  
Vol 20 (03) ◽  
pp. 1340003 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Quantum Discord ◽  
Open Systems ◽  
Vacuum State ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Reservoir Model ◽  
Bipartite State ◽  
Thermal Environments ◽  
Gaussian Input ◽  
Gaussian Quantum Discord

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable quantum discord for a system consisting of two non-interacting bosonic modes embedded in two independent thermal environments. We describe the evolution of discord in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed vacuum state, we analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal reservoirs. For an initial separable pure state, the Gaussian quantum discord is zero and it keeps this value during the whole evolution of the system.

scholarly journals Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 380 ◽  
Author(s):  
Naomichi Hatano ◽  
Gonzalo Ordonez
Keyword(s):  
Time Reversal ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Functional Space ◽  
Time Reversal Symmetry ◽  
Arrow Of Time ◽  
Initial State ◽  
Resonant States ◽  
Complex Eigenvalues

It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called “unphysical”, they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for t > 0 ; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamic ending at a time-reversal symmetric final state is dominated by the anti-resonant states for t < 0 .

scholarly journals Toppling Pencils—Macroscopic Randomness from Microscopic Fluctuations

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1046
Author(s):  
Thomas Dittrich ◽  
Santiago Peña Martínez
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Harmonic Oscillators ◽  
Bistable System ◽  
Asymptotic State ◽  
Initial State ◽  
Central System ◽  
Bistable Systems ◽  
Stable Equilibria ◽  
The Right

We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number N of harmonic oscillators. Solving the time-reversal invariant Hamiltonian equations of motion numerically, we show that for N=1, the system exhibits a transition with increasing coupling strength from integrable to chaotic motion, following the Kolmogorov-Arnol’d-Moser (KAM) scenario. Raising N to values of the order of 10 and higher, the dynamics crosses over to a quasi-relaxation, approaching either one of the stable equilibria at the two minima of the potential. We corroborate the irreversibility of this relaxation on other characteristic timescales of the system by recording the time dependences of autocorrelation, partial entropy, and the frequency of jumps between the wells as functions of N and other parameters. Preparing the central system in the unstable equilibrium at the top of the barrier and the bath in a random initial state drawn from a Gaussian distribution, symmetric under spatial reflection, we demonstrate that the decision whether to relax into the left or the right well is determined reproducibly by residual asymmetries in the initial positions and momenta of the bath oscillators. This result reconciles the randomness and spontaneous symmetry breaking of the asymptotic state with the conservation of entropy under canonical transformations and the manifest symmetry of potential and initial condition of the bistable system.

Study of time dependence of magnetoresistance in multilayer nanostructures with magnetization perpendicular to film plane

2020 ◽  
Vol 25 (4) ◽  
pp. 28-35
Author(s):  
Marina V. Mamonova ◽  
Vladimir V. Prudnikov ◽  
Pavel V. Prudnikov ◽  
Yulia K. Evstafyeva
Keyword(s):  
Time Dependence ◽  
Film Plane ◽  
Time Behavior ◽  
Initial State ◽  
Multilayer Nanostructures ◽  
Ferromagnetic Films ◽  
Time Regime ◽  
Long Time ◽  
Initial States

Influence of different initial states on time behavior of magnetoresistance is studied for nanostructures with magnetization out of films plane. It is shown that two-time dependence of the magnetoresistance reaches plateau in long-time regime with values, which depend on initial state, thickness of ferromagnetic films and temperature.

scholarly journals Исследование влияния начальных состояний, анизотропии и дефектов структуры на неравновесное критическое поведение трехмерной модели Гейзенберга

2020 ◽  
Vol 62 (5) ◽  
pp. 732
Author(s):  
В.В. Прудников ◽  
П.В. Прудников ◽  
А.С. Лях
Keyword(s):  
Autocorrelation Function ◽  
Heisenberg Model ◽  
Easy Axis ◽  
Three Dimensional ◽  
Structural Defects ◽  
Aging Effects ◽  
Initial State ◽  
Slowing Down ◽  
Time Regime ◽  
Long Time

A numerical Monte Carlo study of different initial states, magnetic anisotropy of “easy axis” type, and structural defects influence on non-equilibrium critical behavior of the classical three-dimensional Heisenberg model has been carried out. Analysis of time dependence of the magnetization and the autocorrelation function for isotropic Heisenberg model has shown strong influence of initial states on relaxation of the magnetization and aging effects in behavior of the autocorrelation function, which are characterized by anomalous slowing down of relaxation and correlation in system with increasing waiting time. Study of the anisotropic Heisenberg model with magnetic anisotropy of “easy axis” type has revealed that behavior of the magnetization and autocorrelation function in long-time regime is characterized by critical exponents of the three-dimensional Ising model and more fast decay of the autocorrelation function than for isotropic Heisenberg model. It has been revealed that in structurally disordered isotropic Heisenberg model relaxing from the low-temperature initial state, the significant changes of non-equilibrium aging phenomena in comparison with pure model are observed due to the pinning of domain walls on defects. It has been shown that during this relaxation process a strong slowing-down of time dependence of the autocorrelation function is realized. As a result, superaging effects occur in long-term behavior of the autocorrelation function with values of the superaging exponent μ=2.6(1). During evolution of system from high-temperature initial state, the presence of structural defects leads to increase of aging effects in aging regime, but their influence is found irrelevant in long-time regime.

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