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

International Journal of Modern Physics B

Interplay of dissipation and memory in the quantum Langevin dynamics of a spin in a magnetic field

Suraka Bhattacharjee, Koushik Mandal, Supurna Sinha

Published Feb 28, 2023• 1 citation
Publisher

Abstract

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and coupled to a bath. We have considered two models for the bath: an Ohmic bath model and a non-Markovian Drude bath model with finite memory. The effect of finite memory on the dynamics of the quantum spin is studied in detail. In particular, we have studied the effect of memory on the expectation values of the magnetic moment and the spin correlation functions. The time evolution study of the spin correlation functions shows that the correlation functions exhibit a damped oscillatory behavior with the randomization time being determined by the damping rate. We have analytically shown that the damping gets affected by the finite memory time when the bath retains memory of the interaction with the system. We also analyze the spin response function of the system for the Ohmic bath. Our results qualitatively agree with the findings in spin noise spectroscopy experiments and our predictions can be tested in future ultracold atom experiments.

DOI
10.1142/s021797922450005x

Related papers

Quantum Langevin Equation of a spin in a magnetic field : an analysis

Suraka Bhattacharjee, Koushik Mandal, Supurna Sinha

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and study its dynamics in the Markovian limit using the Ohmic bath model. We extend our analysis to the Drude bath with a finite memory. We study the time evolution of the expectation values of the magnetic moments. The spin auto-correlation functions exhibit a damped oscillatory behaviour with the randomization time being determined by the damping rate and also the memory time for the Drude bath model. We also analyse the spin response function of the system for the Ohmic bath model. Our results are consistent with findings in cold atom experiments. In addition we make predictions which can be tested in future ultra cold atom experiments.

arXiv:2208.12989•Aug 27, 2022•0 citations

Non-equilibrium Quantum Langevin dynamics of a charged particle in a magnetic field : Response function, position-velocity and velocity autocorrelation functions

Suraka Bhattacharjee, Urbashi Satpathi, Supurna Sinha

We use the Quantum Langevin equation as a starting point to study the response function, the position-velocity correlation function and the velocity autocorrelation function of a charged Quantum Brownian particle in a magnetic field coupled to a bath. We study two bath models -- the Ohmic bath model and the Drude bath model and make a detailed comparison in various time-temperature regimes. For both bath models there is a competition between the cyclotron frequency and the viscous damping rate giving rise to a transition from an oscillatory to a monotonic behaviour as the damping rate is increased. In the zero point fluctuation dominated low temperature regime, non-trivial noise correlations lead to some interesting features in this transition. We study the role of the memory time scale which comes into play in the Drude model and study the effect of this additional time scale. We discuss the experimental implications of our analysis in the context of experiments in cold ions.

•May 14, 2021•0 citations

Decoherence of a quantum magneto-oscillator: Effect of field-bath interaction

Koushik Mandal, Suraka Bhattacharjee, Supurna Sinha

We investigate the quantum dissipative dynamics of a charged magneto-oscillator(CMO) coupled to a heat bath of harmonic oscillators in the presence of an additional field-bath interaction. The problem is formulated within the framework of the generalized quantum Langevin equation, where the external confining potential modifies the random force correlations and the memory kernel of the environment, and the effective spring constant. Using the corresponding non-Markovian master equation, we examine the influence of the field-bath coupling on the temporal decay of the reduced density matrix of the system. We show that the additional interaction leads to an enhancement of the decoherence rate by altering the dissipative response of the bath. Thus our results shed light on the role of field-bath coupling in the quantum to classical transition of a CMO. The resulting fluctuation-dissipation relation is analyzed, and the position autocorrelation, position-velocity correlation and velocity autocorrelation are obtained explicitly. The dependence of these experimentally accessible quantities on the field-bath coupling parameter is discussed. We outline an experimental proposal for testing our theoretical predictions. The study sheds light on reservoir engineering which is central to quantum technologies.

quant-pharXiv:2607.11137•Jul 14, 2026•0 citations

Non-equilibrium quantum Langevin dynamics of orbital diamagnetic moment

Urbashi Satpathi, Supurna Sinha

Abstract We investigate the time dependent orbital diamagnetic moment of a charged particle in a magnetic field in a viscous medium via the quantum Langevin equation. We study how the interplay between the cyclotron frequency and the viscous damping rate governs the dynamics of the orbital magnetic moment in the high temperature classical domain and the low temperature quantum domain for an Ohmic bath. These predictions can be tested via state of the art cold atom experiments with hybrid traps for ions and neutral atoms. We also study the effect of a confining potential on the dynamics of the magnetic moment. We notice that the rate of approach of the diamagnetic moment to the Bohr–van Leeuwen limit is higher in the presence of a potential compared to a situation where there is no confinement. We obtain the expected Bohr–van Leeuwen limit in the high temperature, asymptotic time ( , where is the viscous damping coefficient) limit.

arXiv:1809.10370•Journal of Statistical Mechanics Theory and Experiment•Jun 1, 2019•4 citations

Magnetic-field effects on the motion of a charged particle in a heat bath

X. L. Li, G. W. Ford, Robert F. O’Connell

In a recent paper, Ford, Lewis, and O'Connell [Phys. Rev. A 37, 4419 (1988)] considered a charged quantum particle moving in an arbitrary potential and linearly coupled to a heat bath, and they showed that the macroscopic equation describing the time development of the particle motion is in the form of a quantum generalized Langevin equation. We generalize these results to include the presence of an external magnetic field. We find that the magnetic field manifests itself in the presence of an additional term in the Langevin equation, which is the quantum generalization of the Lorentz force, but the magnetic field does not affect the memory function nor the random force appearing in the quantum Langevin equation. It follows that the noise-noise autocorrelation function, as well as the nonequal time commutator of the noise, is the same as that in the absence of a magnetic field. The case of a blackbody radiation heat bath is shown to be easily analyzed as a special case of our general formalism.

Physical Review A•May 1, 1990•48 citations

Spin-boson model under dephasing: Markovian versus non-Markovian dynamics

Naushad Ahmad Kamar, Daniel A. Paz, Mohammad F. Maghrebi

The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.

arXiv:2305.00110•Physical review. B./Physical review. B•Aug 12, 2024•6 citations
We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and coupled to a bath. We have considered two models for the bath: an Ohmic bath model and a non-Markovian Drude bath model with finite memory. The effect of finite memory on the dynamics of the quantum spin is studied in detail. In particular, we have studied the effect of memory on the expectation values of the magnetic moment and the spin correlation functions. The time evolution study of the spin correlation functions shows that the correlation functions exhibit a damped oscillatory behavior with the randomization time being determined by the damping rate. We have analytically shown that the damping gets affected by the finite memory time when the bath retains memory of the interaction with the system. We also analyze the spin response function of the system for the Ohmic bath. Our results qualitatively agree with the findings in spin noise spectroscopy experiments and our predictions can be tested in future ultracold atom experiments.
We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and study its dynamics in the Markovian limit using the Ohmic bath model. We extend our analysis to the Drude bath with a finite memory. We study the time evolution of the expectation values of the magnetic moments. The spin auto-correlation functions exhibit a damped oscillatory behaviour with the randomization time being determined by the damping rate and also the memory time for the Drude bath model. We also analyse the spin response function of the system for the Ohmic bath model. Our results are consistent with findings in cold atom experiments. In addition we make predictions which can be tested in future ultra cold atom experiments.
We use the Quantum Langevin equation as a starting point to study the response function, the position-velocity correlation function and the velocity autocorrelation function of a charged Quantum Brownian particle in a magnetic field coupled to a bath. We study two bath models -- the Ohmic bath model and the Drude bath model and make a detailed comparison in various time-temperature regimes. For both bath models there is a competition between the cyclotron frequency and the viscous damping rate giving rise to a transition from an oscillatory to a monotonic behaviour as the damping rate is increased. In the zero point fluctuation dominated low temperature regime, non-trivial noise correlations lead to some interesting features in this transition. We study the role of the memory time scale which comes into play in the Drude model and study the effect of this additional time scale. We discuss the experimental implications of our analysis in the context of experiments in cold ions.
We investigate the quantum dissipative dynamics of a charged magneto-oscillator(CMO) coupled to a heat bath of harmonic oscillators in the presence of an additional field-bath interaction. The problem is formulated within the framework of the generalized quantum Langevin equation, where the external confining potential modifies the random force correlations and the memory kernel of the environment, and the effective spring constant. Using the corresponding non-Markovian master equation, we examine the influence of the field-bath coupling on the temporal decay of the reduced density matrix of the system. We show that the additional interaction leads to an enhancement of the decoherence rate by altering the dissipative response of the bath. Thus our results shed light on the role of field-bath coupling in the quantum to classical transition of a CMO. The resulting fluctuation-dissipation relation is analyzed, and the position autocorrelation, position-velocity correlation and velocity autocorrelation are obtained explicitly. The dependence of these experimentally accessible quantities on the field-bath coupling parameter is discussed. We outline an experimental proposal for testing our theoretical predictions. The study sheds light on reservoir engineering which is central to quantum technologies.
Abstract We investigate the time dependent orbital diamagnetic moment of a charged particle in a magnetic field in a viscous medium via the quantum Langevin equation. We study how the interplay between the cyclotron frequency and the viscous damping rate governs the dynamics of the orbital magnetic moment in the high temperature classical domain and the low temperature quantum domain for an Ohmic bath. These predictions can be tested via state of the art cold atom experiments with hybrid traps for ions and neutral atoms. We also study the effect of a confining potential on the dynamics of the magnetic moment. We notice that the rate of approach of the diamagnetic moment to the Bohr–van Leeuwen limit is higher in the presence of a potential compared to a situation where there is no confinement. We obtain the expected Bohr–van Leeuwen limit in the high temperature, asymptotic time ( , where is the viscous damping coefficient) limit.
In a recent paper, Ford, Lewis, and O'Connell [Phys. Rev. A 37, 4419 (1988)] considered a charged quantum particle moving in an arbitrary potential and linearly coupled to a heat bath, and they showed that the macroscopic equation describing the time development of the particle motion is in the form of a quantum generalized Langevin equation. We generalize these results to include the presence of an external magnetic field. We find that the magnetic field manifests itself in the presence of an additional term in the Langevin equation, which is the quantum generalization of the Lorentz force, but the magnetic field does not affect the memory function nor the random force appearing in the quantum Langevin equation. It follows that the noise-noise autocorrelation function, as well as the nonequal time commutator of the noise, is the same as that in the absence of a magnetic field. The case of a blackbody radiation heat bath is shown to be easily analyzed as a special case of our general formalism.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.