Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Classical limit: localization induced by noise.

Blanchard Ph, Michele Pasquini, Maurizio Serva

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces decoherence and suppression of tunnelling. These features are necessary ingredients for classicality, but we believe that classicality also implies that quantum delocalized states spontaneously evolve into localized ones. We then show that this evolution takes place only when both noise and non linearity in the equations are present.

Related papers

Decoherence, delocalization, and irreversibility in quantum chaotic systems

K. Shiokawa, B. L. Hu

Decoherence in quantum systems which are classically chaotic is studied. The Arnold cat map and the quantum kicked rotor are chosen as examples of linear and nonlinear chaotic systems. The Feynman-Vernon influence functional formalism is used to study the effect of the environment on the system. It is well known that quantum coherence can obliterate chaotic behavior in the corresponding classical system. But interaction with an environment can under general circumstances quickly diminish quantum coherence and reenact classical chaotic behavior. How effectively decoherence works to sustain chaos, and how the resultant behavior qualitatively differs from the quantum picture, depending on the coupling of the system with the environment and the spectral density and temperature of the environment. We show how recurrence in the quantum cat map is lost and classical ergodicity is recovered due to the effect of the environment. Quantum coherence and diffusion suppression are instrumental to dynamical localization for the kicked rotor. We show how environment-induced effects can destroy this localization. Such effects can also be understood as resulting from external noises driving the system. Peculiar to decohering chaotic systems is the apparent transition from reversible to irreversible dynamics. We show such transitions in the quantum cat map and the kicked rotor and distinguish it from apparent irreversibility originating from dynamical instability and imprecise measurements. By performing a time reversal on and following the quantum kicked rotor dynamics numerically, we show how the otherwise reversible quantum dynamics acquires an arrow of time upon the introduction of noise or interaction with an environment.

arXiv:chao-dyn/9503009•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 1, 1995•42 citations

Decoherence and localization in tunneling process under influence of one external degree of freedom

Quanlin Jie, Bambi Hu, Guangjong Dong

We investigate numerically the tunneling effect under influence of another particle in a double well system. Such influence from only one degree of freedom makes decoherence and quantum-classical transition, i.e., suppression of the tunneling effect. The decoherence happens even for cases that the influence is from a particle of very small mass, and it has virtually no effect in the corresponding classical dynamics. There are cases similar to dynamical localization that the suppressed tunneling rate is several times smaller than the classical counterpart. This result is relevant for understanding quantitatively the dynamical process of decoherence and quantum to classical transition.

arXiv:quant-ph/0601025•Jan 4, 2006•0 citations

Macroscopic tunneling, decoherence and noise-induced activation

Fernando C. Lombardo, Diana Monteoliva, Paula I. Villar

Abstract. We study the effects of the environment at zero temperature on tunneling in an open system described by a static double-well potential. We show that the evolution of the system in an initial Schrödinger cat state, can be summarized in terms of three main physical phenomena, namely decoherence, quantum tunneling and noise-induced activation. Using large-scale numerical simulations, we obtain a detailed picture of the main stages of the evolution and of the relevant dynamical processes. The tunneling of a particle through a potential barrier is a fundamental effect in quantum mechanics. Macroscopic quantum tunneling can be associated with the tunneling of a many-body wavefunction through a potential barrier, and therefore provides a more stringent test of the validity of quantum mechanics than one particle case. One place where the study of macroscopic quantum tunneling is experimentally accesible is in the tunneling of a Bose-Einstein condensate (BEC) out of an optical trap. These systems have a controllable number of atoms and hence straddle the boundary between microscopic and macroscopic, and hence between quantum and classical systems. Proposals to perform interference experiments using confined atoms

•Jan 1, 2006•1 citation

Qubit dynamics with classical noise

Qin Huang, Marco Merkli

We study the evolution of a qubit evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. We show that the noise-averaged qubit density matrix converges to a final state, in the limit of large times t. The convergence speed is polynomial in 1/t, with a power depending on the regularity of the noise probability density and its low frequency behaviour. We evaluate the final state explicitly. We show that in the two regimes of weak and of strong off-diagonal noise, the process implements the dephasing channel in the energy- (localized) and the delocalized basis, respectively.

arXiv:2009.03517•Physics Open•Sep 24, 2020•5 citations

Quantum dynamics with classical noise

Qin Huang

In this thesis, we study the evolution of qubits evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. For a single qubit exposed to such noise, we show that the noise-averaged qubit density matrix converges to a specific final state, in the limit of large time t. We find that the convergence speed is polynomial in 1=t, with a power that depends on the regularity and the low frequency behaviour of the noise probability density. We evaluate the final state explicitly in the regimes of weak and strong off-diagonal noise. We show that the process implements the well-known dephasing channel in the localized and delocalized basis, respectively. Furthermore, we consider the evolution of the entanglement of two (or more) qubits subject to Gaussian noises with varying means and variances. We consider two different cases: individual noise where each qubit feels an independent noise, and common noise where all qubits are subjected to the same noise. We find the following characteristics of entanglement, measured by the concurrence of qubits. Initially entangled states lose their amount of entanglement in time due to the presence of the noise. The decay of entanglement happens more quickly for common noise than for individual noise. We also detect creation of entanglement due to the common noise: for some initially disentangled states, entanglement is created for intermediate times and then decays to zero in the long time again.

•Jan 26, 2022•0 citations

Quantum Mechanics with Spontaneous Localization

T. Weber

One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.

•Jan 1, 1991•0 citations
We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces decoherence and suppression of tunnelling. These features are necessary ingredients for classicality, but we believe that classicality also implies that quantum delocalized states spontaneously evolve into localized ones. We then show that this evolution takes place only when both noise and non linearity in the equations are present.
Decoherence in quantum systems which are classically chaotic is studied. The Arnold cat map and the quantum kicked rotor are chosen as examples of linear and nonlinear chaotic systems. The Feynman-Vernon influence functional formalism is used to study the effect of the environment on the system. It is well known that quantum coherence can obliterate chaotic behavior in the corresponding classical system. But interaction with an environment can under general circumstances quickly diminish quantum coherence and reenact classical chaotic behavior. How effectively decoherence works to sustain chaos, and how the resultant behavior qualitatively differs from the quantum picture, depending on the coupling of the system with the environment and the spectral density and temperature of the environment. We show how recurrence in the quantum cat map is lost and classical ergodicity is recovered due to the effect of the environment. Quantum coherence and diffusion suppression are instrumental to dynamical localization for the kicked rotor. We show how environment-induced effects can destroy this localization. Such effects can also be understood as resulting from external noises driving the system. Peculiar to decohering chaotic systems is the apparent transition from reversible to irreversible dynamics. We show such transitions in the quantum cat map and the kicked rotor and distinguish it from apparent irreversibility originating from dynamical instability and imprecise measurements. By performing a time reversal on and following the quantum kicked rotor dynamics numerically, we show how the otherwise reversible quantum dynamics acquires an arrow of time upon the introduction of noise or interaction with an environment.
We investigate numerically the tunneling effect under influence of another particle in a double well system. Such influence from only one degree of freedom makes decoherence and quantum-classical transition, i.e., suppression of the tunneling effect. The decoherence happens even for cases that the influence is from a particle of very small mass, and it has virtually no effect in the corresponding classical dynamics. There are cases similar to dynamical localization that the suppressed tunneling rate is several times smaller than the classical counterpart. This result is relevant for understanding quantitatively the dynamical process of decoherence and quantum to classical transition.
Abstract. We study the effects of the environment at zero temperature on tunneling in an open system described by a static double-well potential. We show that the evolution of the system in an initial Schrödinger cat state, can be summarized in terms of three main physical phenomena, namely decoherence, quantum tunneling and noise-induced activation. Using large-scale numerical simulations, we obtain a detailed picture of the main stages of the evolution and of the relevant dynamical processes. The tunneling of a particle through a potential barrier is a fundamental effect in quantum mechanics. Macroscopic quantum tunneling can be associated with the tunneling of a many-body wavefunction through a potential barrier, and therefore provides a more stringent test of the validity of quantum mechanics than one particle case. One place where the study of macroscopic quantum tunneling is experimentally accesible is in the tunneling of a Bose-Einstein condensate (BEC) out of an optical trap. These systems have a controllable number of atoms and hence straddle the boundary between microscopic and macroscopic, and hence between quantum and classical systems. Proposals to perform interference experiments using confined atoms
We study the evolution of a qubit evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. We show that the noise-averaged qubit density matrix converges to a final state, in the limit of large times t. The convergence speed is polynomial in 1/t, with a power depending on the regularity of the noise probability density and its low frequency behaviour. We evaluate the final state explicitly. We show that in the two regimes of weak and of strong off-diagonal noise, the process implements the dephasing channel in the energy- (localized) and the delocalized basis, respectively.
In this thesis, we study the evolution of qubits evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. For a single qubit exposed to such noise, we show that the noise-averaged qubit density matrix converges to a specific final state, in the limit of large time t. We find that the convergence speed is polynomial in 1=t, with a power that depends on the regularity and the low frequency behaviour of the noise probability density. We evaluate the final state explicitly in the regimes of weak and strong off-diagonal noise. We show that the process implements the well-known dephasing channel in the localized and delocalized basis, respectively. Furthermore, we consider the evolution of the entanglement of two (or more) qubits subject to Gaussian noises with varying means and variances. We consider two different cases: individual noise where each qubit feels an independent noise, and common noise where all qubits are subjected to the same noise. We find the following characteristics of entanglement, measured by the concurrence of qubits. Initially entangled states lose their amount of entanglement in time due to the presence of the noise. The decay of entanglement happens more quickly for common noise than for individual noise. We also detect creation of entanglement due to the common noise: for some initially disentangled states, entanglement is created for intermediate times and then decays to zero in the long time again.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.