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Backflow for open quantum systems of two identical particles

S. V. Mousavi, Salvador Miret-Artés

Published Apr 14, 2020• 1 citation
OpenAlex

Abstract

In this work, quantum backflow for open quantum systems of two identical spinless particles is addressed within the Caldeira-Leggett (CL) approach under the presence of an opposing force and by using single Gaussian and non-Gaussian wave packets. Backflow is shown to be reduced for small opposing forces, relaxation rate, temperature and a certain degree of non-Gaussianity, but never suppressed. This effect seems to be persistent at long times when considering only one wave packet, implying that interference plays no role. This remarkable behavior is attributed to the time dependence of the width of the probability density expressed in terms of relaxation rate and temperature through the diffusion coefficient. For identical spinless particles, the so-called single-particle probability density and simultaneous/joint detection probability are evaluated. Backflow is found to be occurred only for the dissipative case, being again persistent in time only without an opposing force. Our calculations show that identical spinless fermions display a higher amount of backflow with respect to identical spinless bosons and distinguishable particles. With damping and temperature, the decoherence process, loss of being indistinguishable, is settled gradually with time. At decoherence, the nature of the particles is no longer relevant.

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James M. Yearsley, J. J. Halliwell, R. Hartshorn +1 more

We investigate the backflow effect in elementary quantum mechanics---the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We compute the current and flux for states consisting of superpositions of Gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz et al. [Penz, Gr\"ubl, Kreidl, and Wagner, J. Phys. A 39, 423 (2006)], we find two nontrivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backward flux equal to about 70$%$ of the maximum possible backflow, a dimensionless number ${c}_{bm}\ensuremath{\approx}0.04$, discovered by Bracken and Melloy [Bracken and Melloy, J. Phys. A 27, 2197 (1994)]. This number has the unusual property of being independent of $\ensuremath{\hbar}$ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We discuss some specific measurement models in which backflow may be identified in certain measurable probabilities.

arXiv:1202.1783•Physical Review A•Oct 15, 2012•42 citations
In this work, quantum backflow for open quantum systems of two identical spinless particles is addressed within the Caldeira-Leggett (CL) approach under the presence of an opposing force and by using single Gaussian and non-Gaussian wave packets. Backflow is shown to be reduced for small opposing forces, relaxation rate, temperature and a certain degree of non-Gaussianity, but never suppressed. This effect seems to be persistent at long times when considering only one wave packet, implying that interference plays no role. This remarkable behavior is attributed to the time dependence of the width of the probability density expressed in terms of relaxation rate and temperature through the diffusion coefficient. For identical spinless particles, the so-called single-particle probability density and simultaneous/joint detection probability are evaluated. Backflow is found to be occurred only for the dissipative case, being again persistent in time only without an opposing force. Our calculations show that identical spinless fermions display a higher amount of backflow with respect to identical spinless bosons and distinguishable particles. With damping and temperature, the decoherence process, loss of being indistinguishable, is settled gradually with time. At decoherence, the nature of the particles is no longer relevant.
In this work, dissipative quantum backflow is studied for a superposition of two stretched Gaussian wave packets and two identical spinless particles within the Caldirola-Kanai framework. Backflow is mainly an interference process and dissipation is not able to suppress it in the first case. For two identical spinless particles, apart from interference terms, the symmetry of the wave function seems to be crucial in this dynamics. The combined properties make bosons display this effect, even for the dissipative regime but, for fermions, backflow is not exhibited in any regime, dissipative and nodissipative. The anti-symmetric character of the corresponding wave function seems to be strong enough to prevent it. For bosons, backflow is also analyzed in terms of fidelity of one-particle states which is a well-known property of two quantum states. At very small values of fidelity, this effect is not seen even for bosons.
In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira–Leggett formalism and under the presence of a linear potential is studied. As a dimensionless measure of decoherence, purity, a quantity appearing in the definition of the linear entropy, is studied taking into account the role of the stretching parameter. Special emphasis is on the open dynamics of the well-known cat states and bosons and fermions compared to distinguishable particles. For the cat state, while the stretching parameter speeds up the decoherence, the external linear potential strength does not affect the decoherence time; only the interference pattern is shifted. Furthermore, the interference pattern is not observed for minimum-uncertainty-product-Gaussian wave packets in the momentum space. Concerning bosons and fermions, the question we have addressed is how the symmetry of the wave functions of indistinguishable particles is manifested in the decoherence process, which is understood here as the loss of being indistinguishable due to the gradual emergence of classical statistics with time. We have observed that the initial bunching and anti-bunching character of bosons and fermions, respectively, in the momentum space are not preserved as a function of the environmental parameters, temperature, and damping constant. However, fermionic distributions are slightly broader than the distinguishable ones and these similar to the bosonic distributions. This general behavior could be interpreted as a residual reminder of the symmetry of the wave functions in the momentum space for this open dynamics.
Quantum backflow is the classically forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of NNN free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the NNN identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of NNN.
Abstract This thesis has two parts, in the first, the Caldeira-Leggett model is introduced; its derivation and general consequences are explored following a paper by Caldeira and Leggett[1]. An operator-formalism shortcut through some of the more mathematically cumbersome parts of the derivation of the model is also developed. The correlation of the force resulting from reservoir-interaction is examined in the high- and low-temperature limits, and the Langevin equation is shown to emerge in the classical limit.Abstract The second part introduces decoherence through a thought experiment that demonstrates the destructive effect of random phase shifts on interference terms, and then follows another paper by Caldeira and Leggett[2] in applying their model further to study the phenomenon of dissipative decoherence. The time-evolution of the interference terms in a superposition of Gaussian wave packets in a harmonic oscillator potential is studied when interacting with a heat bath, and they are shown to vanish at a rate much faster than the relaxation of the system.
Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the effect is intrinsically small, with less than 4% of the probability able to flow backward, and (ii) it requires wave packets with a well-defined momentum direction, which are difficult both to prepare and to verify under realistic, noisy conditions. Here, we overcome these challenges by introducing a general formulation of quantum backflow applicable to arbitrary momentum distributions. The framework recovers the standard backflow limit for unidirectional states and identifies general backflow as probability flow exceeding that predicted by the particle's momentum distribution alone. We show that this excess can reach nearly 13%, surpassing the standard backflow bound by more than a factor of three. Furthermore, we extend the framework to the closely related phenomenon of quantum reentry, provide explicit examples of quantum states exhibiting large general backflow and reentry, and discuss the foundational implications of these nonclassical effects. Our results open a pathway toward the experimental observation of quantum backflow in realistic settings.
We investigate the backflow effect in elementary quantum mechanics---the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We compute the current and flux for states consisting of superpositions of Gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz et al. [Penz, Gr\"ubl, Kreidl, and Wagner, J. Phys. A 39, 423 (2006)], we find two nontrivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backward flux equal to about 70% of the maximum possible backflow, a dimensionless number ${c}_{bm}\ensuremath{\approx}0.04$, discovered by Bracken and Melloy [Bracken and Melloy, J. Phys. A 27, 2197 (1994)]. This number has the unusual property of being independent of $\ensuremath{\hbar}$ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We discuss some specific measurement models in which backflow may be identified in certain measurable probabilities.