arXiv subjects

Malay Bandyopadhyay

Publications and source records attributed to Malay Bandyopadhyay.

At least 37 records · Page 2Linked to original sources

arXiv2022

Quantum counterpart of energy equipartition theorem for fermionic systems

In this brief report, following the recent developments on formulating a quantum analogue of the classical energy equipartition theorem for open systems where the heat bath comprises of independent oscillators, i.e. bosonic degrees of freedom, we present an analogous result for fermionic systems. The most general case where the system is connected to multiple reservoirs is considered and the mean energy in the steady state is expressed as an integral over the reservoir frequencies. Physically this would correspond to summing over the contributions of the bath degrees of freedom to the mean energy of the system over a suitable distribution function $ρ(ω)$ dependent on the system parameters. This result holds for nonequilibrium steady states, even in the nonlinear regime far from equilibrium. We also analyze the zero temperature behaviour and low temperature corrections to the mean energy of the system.

cond-mat.stat-mech↗

arXiv2021

Quantum counterpart of energy equipartition theorem for a dissipative charged magneto-oscillator: Effect of dissipation, memory, and magnetic field

In this paper, we formulate and study the quantum counterpart of the energy equipartition theorem for a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a passive quantum heat bath through coordinate variables. The bath is modelled as a collection of independent quantum harmonic oscillators. We derive the closed form expressions for the mean kinetic and potential energies of the charged-dissipative-magneto-oscillator in the form $E_k = \langle \mathcal{E}_k \rangle$ and $E_p = \langle \mathcal{E}_p \rangle$ respectively, where $\mathcal{E}_k$ and $\mathcal{E}_p$ denote the average kinetic and potential energies of individual thermostat oscillators. The net averaging is two-fold, the first one being over the Gibbs canonical state for the thermostat, giving $\mathcal{E}_k$ and $\mathcal{E}_p$ and the second one denoted by $\langle . \rangle$ being over the frequencies $ω$ of the bath oscillators which contribute to $E_k$ and $E_p$ according to probability distributions $\mathcal{P}_k(ω)$ and $\mathcal{P}_p(ω)$ respectively. The relationship of the present quantum version of the equipartition theorem with that of the fluctuation-dissipation theorem (within the linear-response theory framework) is also explored. Further, we investigate the influence of the external magnetic field and the effect of different dissipation processes through Gaussian decay, Drude and radiation bath spectral density functions, on the typical properties of $\mathcal{P}_k(ω)$ and $\mathcal{P}_p(ω)$. Finally, the role of system-bath coupling strength and the memory effect is analyzed in the context of average kinetic and potential energies of the dissipative charged magneto-oscillator.

cond-mat.stat-mech↗

arXiv2021

Contact geometry and quantum thermodynamics of nanoscale steady states

We develop a geometric formalism suited for describing the quantum thermodynamics of a certain class of nanoscale systems (whose density matrix is expressible in the McLennan--Zubarev form) at any arbitrary non-equilibrium steady state. It is shown that the non-equilibrium steady states are points on control parameter spaces which are in a sense generated by the steady state Massieu--Planck function. By suitably altering the system's boundary conditions, it is possible to take the system from one steady state to another. We provide a contact Hamiltonian description of such transformations and show that moving along the geodesics of the friction tensor results in a minimum increase of the free entropy along the transformation. The control parameter space is shown to be equipped with a natural Riemannian metric that is compatible with the contact structure of the quantum thermodynamic phase space which when expressed in a local coordinate chart, coincides with the Schlögl metric. Finally, we show that this metric is conformally related to other thermodynamic Hessian metrics which might be written on control parameter spaces. This provides various alternate ways of computing the Schlögl metric which is known to be equivalent to the Fisher information matrix.

cond-mat.stat-mech↗

arXiv2021

Environment dependent vibrational heat transport in molecular Junctions : Rectification, quantum effects, vibrational mismatch

Vibrational heat transport in molecular junctions is a central issue in different contemporary research areas like Chemistry, material science, mechanical engineering, thermoelectrics and power generation. Our model system consists of a chain of molecules which sandwiched between two solids that are maintained at different temperatures. We employ quantum self-consistent reservoir model, which is built on generalized quantum Langevin equation, to investigate quantum effects and far from equilibrium conditions on thermal conduction at nanoscale. The present self-consistent reservoir model can easily mimic the phonon-phonon scattering mechanisms. Different thermal environments are modelled as (i) Ohmic, (ii) sub-Ohmic, and (iii) super-Ohmic environment and their effects are demonstrated for the thermal rectification properties of the system with spring graded or mass graded feature. The behavior of heat current across molecular junctions as a function of chain length, temperature gradient and phonon scattering rate are studied. Further, our analysis reveals the effects of vibrational mismatch between the solids phonon spectra on heat transfer characteristics in molecular junctions for different thermal environments.

cond-mat.stat-mech↗

arXiv2017

Quantum thermodynamic properties of a cold atom coupled to a heat bath in non-Abelian gauge potentials

In this work, we study different quantum thermodynamic functions (QTFs) of a cold atom subjected to an artificial non-Abelian uniform magnetic field and linearly coupled to a quantum heat bath through either usual coordinate-coordinate coupling or through momentum variables. The bath is modelled as a collection of independent quantum harmonic oscillators. In each of the coupling scheme, the effect of the non-Abelian magnetic field on different QTFs are explicitly demonstrated for a U(2) gauge transformation. In each case, we show that the free energy has a different expression than that for the Abelian case. We consider two illustrative heat bath spectrum (Ohmic bath and Drude model) to evaluate explicit closed form expressions of free energy (F), specific heat (C), and entropy (S) in the low temperature limit for each of the above mentioned coupling scheme. The dependence of different QTFs on the non-Abelian magnetic field are pointed out even if the gauge potential is uniform in space.

cond-mat.quant-gas↗

arXiv2017

Barrierless reaction kinetics : Inertial effect on different distribution functions of relevant Brownian functionals

We investigate the effect of inertia on barrierless electronic reactions in solution by suggesting and examining different probability distribution functions (PDF) of relevant Brownian functionals associated with the lifetime and reactivity of the process. Activationless electronic reaction in solution can be modeled as a free Brownian motion with inertial term in the underdamped regime. In this context we suggest several important distribution functions that can characterize the reaction kinetics. Most of the studies on Brownian functional which has vast potential application in diverse fields, are confined in the overdamped regime. To the best of our knowledge, we are attempting first time to incorporate the much important inertial effects on the study of different PDFs related with Brownian functionals of an underdamped Brownian motion with time dependent drift and diffusion coefficients using celebrated backward Fokker-Planck and path decomposition methods. We have explored nontrivial scaling behaviour of different PDFs and calculated explicitly the critical exponents related with the asymptotic limits in time.

cond-mat.stat-mech↗

arXiv2016

Control of Decoherence in different environments : A case study for dissipative magneto-oscillator

In this paper, we analyze two different techniques based on reservoir engineering method and quantum Zeno effect for controlling decoherence of a dissipative charged oscillator in the presence of an external magnetic field. Our main focus is to investigate the sensitiveness of these decoherence control techniques on the details of different environmental spectrum ($J(ω)$), and on the crucial role played by different system and reservoir parameters, e.g., external magnetic field ($r_c$), confinement length ($r_0$), temperature (T), cut-off frequency of reservoir spectrum ($ω_{cut}$), and measurement interval ($τ$). First, we consider the charged quantum oscillator in an initial nonclassical Schrodinger cat state and analyze the non-Markovian dynamics for the magneto-oscillator in contact with Ohmic, sub-Ohmic, and super-Ohmic environments. We show the procedure to control the quantumness of the Schrodinger cat state by tuning the parameters $r_c$, $r_0$, and $J(ω)$. On the other hand, we investigate the effect of nonselective energy measurement process on the mortification of quantumness of an initial Fock-Darwin state of the charged magneto-oscillator. We investigate in details the strategy to manipulate the continuous passage from decay suppression to decay acceleration by engineered reservoirs and by tuning the system or reservoir parameters, e.g., $r_c$, $r_0$, T or $τ$. As a result of that one can control environment induced decoherence (EID).

cond-mat.stat-mech↗

arXiv2016

Study of Brownian functionals in physically motivated model with purely time dependent drift and diffusion

In this paper, we investigate a Brownian motion (BM) with purely time dependent drift and difusion by suggesting and examining several Brownian functionals which characterize the lifetime and reactivity of such stochastic processes. We introduce several probability distribution functions (PDFs) associated with such time dependent BMs. For instance, for a BM with initial starting point $x_0$, we derive analytical expressions for : (i) the PDF $P(t_f|x_0)$ of the first passage time $t_f$ which specify the lifetime of such stochastic process, (ii) the PDF $P(A|x_0)$ of the area A till the first passage time and it provides us numerous valuable information about the effective reactivity of the process, (iii) the PDF $P(M)$ associated with the maximum size M of the BM process before the first passage time, and (iv)the joint PDF $P(M; t_m)$ of the maximum size M and its occurrence time $t_m$ before the first passage time. These distributions are examined for the power law time time dependent drift and diffusion. A simple illustrative example for the stochastic model of water resources availability in snowmelt dominated regions with power law time dependent drift and diffusion is demonstrated in details. We motivate our study with approximate calculation of an unsolved problem of Brownian functionals including inertia.

cond-mat.stat-mech↗

arXiv2015

Brownian motion of classical spins : Anomalous dissipation and generalized Langevin equation

In this work, we analyze the relaxation of a classical spin interacting with a heat bath, starting from the fully dynamical Hamiltonian description. An analogous problem in the framework of generalized Langevin equation (GLE) with anomalous dissipation is analyzed in details. The Fokker-Planck equation corresponding to GLE is derived and the concept of equilibrium probability distribution is analyzed. In this process we have identified few difficulties to obtain equilibrium distribution for the non-Markovian case and the remedy to overcome this difficulty is also discussed.

cond-mat.mes-hall↗

arXiv2015

Order parameter scaling in fluctuation dominated phase ordering

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles (SP) on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile. We study both static and dynamic scaling laws obeyed by the Fourier modes $Q_m$ and find that the mean value obeys the static scaling law $\langle Q_m \rangle \sim L^{-ϕ}f(m/L)$ with $ϕ\simeq2/3$ and $ϕ\simeq 3/5$ with Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution respectively. The full probability distribution $P(Q_m)$ exhibits scaling as well. Further, time-dependent correlation functions such as the steady state auto-correlation and cross-correlations of order parameter components are scaling functions of $t/L^z$, where $L$ is the system size and $z$ is the dynamic exponent with $z=2$ for EW and $z=3/2$ for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and a weak divergence of the flatness as the scaled time approaches zero.

cond-mat.stat-mech↗

arXiv2014

Control of quantum thermodynamic behaviour of a charged magneto oscillator with momentum dissipation

In this work, we expose the role of environment, confinement and external magnetic field ($B$) in determining the low temperature thermodynamic behaviour in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving the momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTF) are obtained at low temperatures for different quantum heat bath characterized by spectral density function, $μ(ω)$. The power law fall of different QTF are in conformity with third law of thermodynamics. But, the sensitiveness of decay i.e. the power of the power law decay explicitly depends on $μ(ω)$. We also separately discuss the influence of confinement and magnetic field on the low temperature behavior of different QTF. In this process we demonstrate how to control low temperature behaviour of anomalous dissipative quantum systems by varying confining length $a$, $B$ and the temperature $T$. Momentum dissipation reduces effective mass of the system and we also discuss its effect on different QTF at low temperatures.

cond-mat.stat-mech↗

arXiv2013

The probe technique far-from-equilibrium: Magnetic field symmetries of nonlinear transport

The probe technique is a simple mean to incorporate elastic and inelastic processes into quantum dynamics. Using numerical simulations, we demonstrate that this tool can be employed beyond the analytically tractable linear response regime, providing a stable solution for the probe parameters: temperature and chemical potential. Adopting four probes: dephasing, voltage, temperature, and voltage-temperature, mimicking different elastic and inelastic effects, we focus on magnetic field and gate voltage symmetries of charge current and heat current in Aharonov-Bohm interferometers, potentially far-from-equilibrium. Considering electron current, we prove analytically that in the linear response regime inelastic scattering processes do not break the Onsager symmetry. Beyond linear response, even (odd) conductance terms obey an odd (even) symmetry with the threading magnetic flux, as long as the system acquires a spatial inversion symmetry. When spatial asymmetry is introduced particle-hole symmetry assures that nonlinear conductance terms maintain certain symmetries with respect to magnetic field and gate voltage. These analytic results are supported by numerical simulations. Analogous results are obtained for the electron heat current. We also demonstrate that a double-dot Aharonov-Bohm interferometer acts as a rectifier when two conditions are met: (i) many-body effects are included, here in the form of inelastic scattering, and (ii) time reversal symmetry is broken.

cond-mat.mes-hall↗

arXiv2013

Magnetic field symmetries of nonlinear transport with elastic and inelastic scattering

We study nonlinear electronic transport symmetries in Aharonov-Bohm interferometers subjected to inelastic scattering effects and show that odd (even) conductance terms are even (odd) in the magnetic field when the junction is (left-right) spatially symmetric. This observation does not hold when an asymmetry is introduced, as we show numerically, but odd conductance terms only manifest a weak breakdown of the magnetic field symmetry. Under elastic dephasing effects, the Onsager-Casimir symmetry is maintained beyond linear response and under spatial asymmetries.

cond-mat.mes-hall↗

arXiv2013

Free energy of a charged oscillator in a magnetic field and coupled to a heat bath through the momentum variables

We obtain an exact formula for the equilibrium free energy of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a heat bath of independent quantum harmonic oscillators through the momentum variables. We show that the free energy has a different expression than that for the coordinate-coordinate coupling between the particle and the heat-bath oscillators. For an illustrative heat-bath spectrum, we evaluate the free energy in the low-temperature limit, thereby showing that the entropy of the charged particle vanishes at zero temperature, in agreement with the third law of thermodynamics.

cond-mat.stat-mech↗

arXiv2012

Flux-dependent occupations and occupation difference in geometrically symmetric and energy degenerate double-dot Aharonov-Bohm interferometers

We study the steady-state characteristics and the transient behavior of the nonequilibrium double-dot Aharonov-Bohm interferometer using analytical tools and numerical simulations. Our simple setup includes noninteracting degenerate quantum dots that are coupled to two biased metallic leads at the same strength. A magnetic flux $Φ$ is piercing the setup perpendicularly. As we tune the degenerate dots energies away from the symmetric point we observe four nontrivial magnetic flux control effects: (i) flux dependency of the dots occupation, (ii) magnetic flux induced occupation difference between the dots, at degeneracy, (iii) the effect of "phase-localization" of the dots coherence holds only at the symmetric point, while in general both real and imaginary parts of the coherence are nonzero, and (iv) coherent evolution survives even when the dephasing strength, introduced into our model using Büttiker probe, is large and comparable to the dots energies and the bias voltage. Moreover, not only finite dephasing strength does not destroy the coherence features, it can provide new type of coherent oscillations. These four phenomena take place when the dots energies are gated, to be positioned away from the symmetric point, demonstrating that the combination of bias voltage, magnetic flux and gating field, can provide delicate controllability over the occupation of each of the quantum dots, and their coherence.

cond-mat.mes-hall↗

arXiv2011

Thermodynamic properties of magneto-anisotropic nanoparticles

The purpose of this paper is to study the thermodynamic equilibrium properties of a collection of non-interacting three-dimensional (3D) magnetically anisotropic nanoparticles in the light of classical statistical physics. Pertaining to the angular dependence ($α$) of the magnetic field with the anisotropy axis, energy landscape plots are obtained which reveal a continuous transition from a double well to a single well for $α=\fracπ{2}$ and show asymmetric bistable shape for other values of $α$. The present analysis is related with the interpretation of equilibrium magnetization and static susceptibility of nanomagnetic system as a function of external magnetic field, $B$, and temperature, $T$. The magnetization and susceptibility confirms the non Langevin behaviour of magneto-anisotropic monodomain particles. The susceptibility analysis establishes the ferromagnetic, antiferromagnetic and paramagnetic like coupling for various $α$. This study reveals the essential role of magneto anisotropic energy in the interpretation of the magnetic behaviour of a collection of noninteracting single domain nanoparticles.

cond-mat.stat-mech↗

arXiv2011

Quantum Langevin equation of a charged oscillator in a magnetic field and coupled to a heat bath through momentum variables

We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.

cond-mat.stat-mech↗

arXiv2011

Quantum heat transfer in harmonic chains with self consistent reservoirs: Exact numerical simulations

We describe a numerical scheme for exactly simulating the heat current behavior in a quantum harmonic chain with self-consistent reservoirs. Numerically-exact results are compared to classical simulations and to the quantum behavior under the linear response approximation. In the classical limit or for small temperature biases our results coincide with previous calculations. At large bias and for low temperatures the quantum dynamics of the system fundamentally differs from the close-to-equilibrium behavior, revealing in particular the effect of thermal rectification for asymmetric chains. Since this effect is absent in the classical analog of our model, we conclude that in the quantum model studied here thermal rectification is a purely quantum phenomenon, rooted in the quantum statistics.

cond-mat.mes-hall↗