arXiv subjects

Sushanta Dattagupta

Publications and source records attributed to Sushanta Dattagupta.

At least 19 recordsLinked to original sources

arXiv2026

Brownian-motion approach to statistical mechanics: Langevin equations, fluctuations, and timescales

We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a paradigm and upon using the Langevin equation(s), we present a brief exposition of the modern areas of stochastic thermodynamics and fluctuation theorems in a manner accessible to a non-expert. This is followed by an analysis of non-Markovian Brownian dynamics via generalized Langevin equation(s) in which we particularly shed light onto its derivation, the emergence of the fluctuation-dissipation relation, and the recently-discovered effective-mass framework.

cond-mat.stat-mech↗

arXiv2026

Spin-orbit coupled spin-boson model : A variational analysis

The spin-boson (SB) model is a standard prototype for quantum dissipation, which we generalize in this work, to explore the dissipative effects on a one-dimensional spin-orbit (SO) coupled particle in the presence of a sub-ohmic bath. We analyze this model by extending the well-known variational polaron approach, revealing a localization transition accompanied by an intriguing change in the spectrum, for which the doubly degenerate minima evolves to a single minimum at zero momentum as the system-bath coupling increases. For translational invariant system with conserved momentum, a continuous magnetization transition occurs, whereas the ground state changes discontinuously. We further investigate the transition of the ground state in the presence of harmonic confinement, which effectively models a quantum dot-like nanostructure under the influence of the environment. In both the scenarios, the entanglement entropy of the spin-sector can serve as a marker for these transitions. Interestingly, for the trapped system, a cat-like superposition state corresponds to maximum entanglement entropy below the transition, highlighting the relevance of the present model for studying the effect of decoherence on intra-particle entanglement in the context of quantum information processing.

cond-mat.stat-mech↗

arXiv2025

Coherence-decoherence interplay in quantum systems due to projective stochastic pulses: The case of Rabi oscillations

The interplay of coherence and decoherence is played out in a three-level quantum system, in which the third level is incoherently coupled to the second one which itself is in coherent interaction with the first level. The study is based on a stochastic scenario in which the coherent, unitary evolution of the system is randomly interrupted by a Poisson-driven pulse sequence. In the absence of an external pulse, the system undergoes coherent, unitary evolution restricted to the subspace spanned by the first level (level $1$) and the second level (level $2$). The application of a pulse induces transitions between the second and the third level (level $3$), thereby introducing non-unitary effects that perturb the otherwise isolated two-level dynamics. The pulses are assumed to have infinitesimal duration, with strengths modeled as random variables that are uncorrelated across different pulses. A representative model for the stochastically-averaged transition (super)operator mimicking the dynamics induced by the application of pulses allows for an analytical derivation of the matrix elements of the averaged density operator. When the system is initially in level $1$, we obtain in particular the temporal behavior of the stay-put probability, that is, the probability $P_1(t)$ that the system is still in level $1$ at time $t$. As a function of time, the quantity $P_1(t)$ exhibits a coherence-to-decoherence crossover behavior. At short times $t \ll 1/λ$, where $λ$ is the average frequency at which pulses are applied to the system, coherent dynamics dominate. Consequently, $P_1(t)$ displays pronounced Rabi-like oscillations. At long times $t \gg 1/λ$, decoherence effects prevail, leading to an exponential decay of the form $P_1(t) \sim \exp(-λt)$.

quant-ph↗

arXiv2025

Decoherence of Morse Oscillator in the Presence of Dissipationless Environment

The much-studied Morse oscillator (MO) is couched here in the context of an open quantum system, in which the interaction with the quantum environment, however, is taken to commute with the subsystem Hamiltonian. The result is decoherence sans dissipation because of dephasing in the off-diagonal elements of the reduced density operator. The analytical results are numerically computed for a range of parameters, for different attributes of decoherence. Finally, comparison is made for the corresponding harmonic system, in order to highlight the significance of anharmonicity in the MO, as far as dependencies on the temperature and the environmental coupling are concerned.

quant-ph↗

arXiv2025

Quantum transport under oscillatory drive with disordered amplitude

We investigate the dynamics of non-interacting particles in a one-dimensional tight-binding chain in the presence of an electric field with random amplitude drawn from a Gaussian distribution, and explicitly focus on the nature of quantum transport. We derive an exact expression for the probability propagator and the mean-squared displacement in the clean limit and generalize it for the disordered case using the Liouville operator method. Our analysis reveals that in the presence a random static field, the system follows diffusive transport; however, an increase in the field strength causes a suppression in the transport and thus results in disorder-induced localization. We further extend the analysis for a time-dependent disordered electric field and show that the dynamics of mean-squared-displacement deviates from the parabolic path as the field strength increases, unlike the clean limit where ballistic transport occurs.

cond-mat.dis-nn↗

arXiv2025

Stochastic thermodynamics and the Ericsson nano engine -- Efficiency from equilibrium results

In this work, we study an Ericsson cycle whose working substance is a charged (quantum) oscillator in a magnetic field that is coupled to a heat bath. The resulting quantum Langevin equations with built-in noise terms encapsulate a thermodynamic structure and allow for the computation of the efficiency of the cycle. We numerically compute the efficiency of the cycle in the quasi-static regime using the steady-state thermodynamic functions of the system. Interestingly, it is found that by increasing the system-bath coupling strength, the efficiency of the cycle can be tuned to a maximum. We also explore the behavior of the efficiency as a function of the pair of magnetic-field values between which the cycle is operated.

cond-mat.mes-hall↗

arXiv2024

Weak-coupling limits of the quantum Langevin equation for an oscillator

The quantum Langevin equation as obtained from the independent-oscillator model describes a strong-coupling situation, devoid of the Born-Markov approximation that is employed in the context of the Gorini-Kossakowski-Sudarshan-Lindblad equation. The question we address is what happens when we implement such 'Born-Markov'-like approximations at the level of the quantum Langevin equation for a harmonic oscillator which carries a noise term satisfying a fluctuation-dissipation theorem. In this backdrop, we also comment on the rotating-wave approximation.

quant-ph↗

arXiv2024

Independent-oscillator model and the quantum Langevin equation for an oscillator: A review

This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, the so-called independent-oscillator model. This is followed by a discussion on the relevant `weak-coupling' limit. In the steady state, we analyze the quantum counterpart of energy equipartition theorem which has generated a considerable amount of interest in recent literature. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion in a harmonic well. Following this, we explore some aspects of dissipative diamagnetism in the context of quantum Brownian oscillators, emphasizing upon the role of confining potentials and also upon the environment-induced classical-quantum crossover. We discuss situations where the system-bath coupling is via the momentum variables by focusing on a gauge-invariant model of momentum-momentum coupling in the presence of a vector potential; for this problem, we derive the quantum Langevin equation and discuss quantum thermodynamic functions. Finally, the topic of fluctuation theorems is discussed (albeit, briefly) in the context of classical and quantum cyclotron motion of a particle coupled to a heat bath.

cond-mat.stat-mech↗

arXiv2023

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We present here a general formulation for the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. Our main focus is the relaxation behavior of the quantum solid of graphene perturbed by an oscillatory electric field. Considering the optical range of the frequency and a considerable amount of the amplitude of the field, one can observe a nonlinear response by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in the form of a spin-Boson model of dissipative quantum statistical mechanics. Mapping the valence and conduction states as the eigenstates of the Pauli spin operators and utilizing the rotating wave approximation to omit off-resonant terms, one can solve the rate equation for the mean population of the conduction and valence states and the mixing matrix elements between them. Our results reveal the nonlinear steady-state regime's population inversion and interband coherence. It is characterized by a single dimensionless parameter that is directly proportional to the incident field strength and inversely proportional to the optical frequency. Our method is also capable of calculating the nonlinear interband optical conductivity of doped and gapped graphene at finite temperatures. The effects of different bath spectra for phonons and electrons are examined in detail. Although our general formulation can address a variety of nonequilibrium response of the two-band system, it also facilitates a connection with phenomenological modeling of nonlinear optical conductivity.

cond-mat.mes-hall↗

arXiv2023

Stochastic resets in the context of a tight-binding chain driven by an oscillating field

In this work, we study in the framework of the so-called driven tight-binding chain (TBC) the issue of quantum unitary dynamics interspersed at random times with stochastic resets mimicking non-unitary evolution due to interactions with the external environment, The driven TBC involves a quantum particle hopping between the nearest-neighbour sites of a one-dimensional lattice and subject to an external forcing field that is periodic in time. We consider the resets to be taking place at exponentially-distributed random times. Using the method of stochastic Liouville equation, we derive exact results for the probability at a given time for the particle to be found on different sites and averaged with respect to different realizations of the dynamics. We establish the remarkable effect of localization of the TBC particle on the sites of the underlying lattice at long times. The system in the absence of stochastic resets exhibits delocalization of the particle, whereby the particle does not have a time-independent probability distribution of being found on different sites even at long times, and, consequently, the mean-squared displacement of the particle about its initial location has an unbounded growth in time. One may induce localization in the bare model only through tuning the ratio of the strength to the frequency of the field to have a special value, namely, equal to one of the zeros of the zeroth order Bessel function of the first kind. We show here that localization may be induced by a far simpler procedure of subjecting the system to stochastic resets.

quant-ph↗

arXiv2022

Bond current in a mesoscopic ring -- signature of decoherence due to classical and quantum noise

A three-site mesoscopic ring provides an ideal setting for an exact calculation of the bond current when the ring is threaded by an Aharonov-Bohm flux. The bond current is a measurable outcome of the coherent properties of the quantum phase. However the coherence is impeded by noise when the ring is put in contact with an environment. This coherence-to-incoherence transition is analyzed in detail here for both classical (Gaussian and telegraphic) and quantum noise and a comparative assessment is made when the quantum noise is governed by a spin-boson Hamiltonian of dissipative quantum mechanics.

cond-mat.stat-mech↗

arXiv2022

Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain

In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical framework to obtain the average density operator of the system at any time during the dynamical evolution. The average is with respect to the classical randomness associated with the random time intervals between successive interactions, which we consider to be independent and identically-distributed random variables. We provide two explicit applications of the formalism in the context of the so-called tight-binding model relevant in various contexts in solid-state physics. In one dimension, the corresponding tight-binding chain models the motion of a charged particle between the sites of a lattice, wherein the particle is for most times localized on the sites, but which owing to spontaneous quantum fluctuations tunnels between nearest-neighbour sites. We consider two representative forms of interactions: stochastic reset of quantum dynamics, in which the density operator is at random times reset to its initial form, and projective measurements performed on the system at random times. In the former case, we demonstrate with our exact results how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement of the particle about its initial location. In the case of projective measurements at random times, we show that repeated projection to the initial state of the particle results in an effective suppression of the temporal decay in the probability of the particle to be found on the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, but which however does not require performing measurements at exactly regular intervals that are hallmarks of such scenarios.

quant-ph↗

arXiv2019

Planar Hall Effect and Anisotropic Magnetoresistance in a polar-polar interface of LaVO$_3$-KTaO$_3$ with strong spin-orbit coupling

Among the perovskite oxide family, KTaO$_3$ (KTO) has recently attracted considerable interest as a possible system for the realization of the Rashba effect. In this work, we improvise a novel conducting interface by juxtaposing KTO with another insulator, namely LaVO$_3$ (LVO) and report planar Hall effect (PHE) and anisotropic magnetoresistance (AMR) measurements. This interface exhibits a signature of strong spin-orbit coupling. Our experimental observation of two fold AMR at low magnetic fields can be intuitively understood using a phenomenological theory for a Rashba spin-split system. At high fields ($\sim$8 T), we see a two fold to four fold transition in the AMR that could not be explained using only Rashba spin-split energy spectra. We speculate that it might be generated through an intricate process arising from the interplay between strong spin-orbit coupling, broken inversion symmetery, relativistic conduction electron and possible uncompensated localized vanadium spins.

cond-mat.mes-hall↗

arXiv2019

Observation of Shubnikov-de Haas Oscillations, Non-trivial Berry Phase, Planar Hall and Anisotropic Magnetoresistance at the conducting interface of EuO-KTaO$_3$

The momentum dependent splitting of spin-bands in an electronic system is known as the "Rashba effect". Systems with the "Rashba effect" possess a Dirac point in momentum space. An electron in a cyclotron orbit enclosing that Dirac point in the reciprocal space gains a "Berry phase". We report here the Shubnikov-de-Haas oscillations (SdH) at the conducting interface of EuO-KTaO$_3$ (KTO). Observed SdH oscillations suggest the presence of two Fermi surfaces. For both the Fermi surfaces, we have seen the presence of a non-trivial "Berry phase" suggesting that the surfaces enclose the "Dirac point". Thus the Berry phase originates from the inner and outer Fermi surfaces of the Rashba spin-split bands. As in topological insulators, two fold planar Hall and anisotropic magnetoresistance have also been observed in EuO-KTO. Analyzing the SdH, Hall and magnetoresistance data, we have drawn a possible band diagram near the Fermi surface.

cond-mat.mes-hall↗

arXiv2019

`Muhammad Ali effect' and incoherent destruction of Wannier-Stark localization in a stochastic field

We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two-level jump process or a telegraph process (TP) which jumps randomly between two values $\pmμ$. In the absence of a static field and in the limit of zero jump rate of the noisy field we find that the dynamics yield Bloch oscillations with frequency $μ$, while with an additional static field $ε$ we find oscillatory motion with a superposition of frequencies $(ε\pm μ)$. On the other hand, when the jump rate is `rapid', and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable `a-priori'. In that case, we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case is a manifestation of what we call the `Muhammad Ali effect'. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias $δp$ in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field $μδp$. This is an example of \emph{incoherent} destruction of Wannier-Stark localization.

cond-mat.dis-nn↗

arXiv2019

Nonlinear Optical Conductivity in Graphene and other 2-Band 2-D Materials

Graphene, Silicene, $\mathrm{MoS}_2$ and other similar two-dimensional structures have unusual electronic properties that lend themselves to exotic device applications. These properties emanate from the fact that the electrons are endowed with Dirac fermion-like attributes. Thus these materials are not only characterized by certain fundamental principles, they also have amazing practical uses. Our emphasis here is on one such basic property concerning nonlinear response to time-dependent electric fields. We set up a first principle quantum master equation for the underlying density operator which is based on microscopic interactions between the Dirac electron with phonons and other electrons. While such an equation has general applicability to a variety of non-equilibrium phenomena in two-band systems, we focus onto the case of nonlinear optical conductivity. The derived results are separately analyzed for graphene, silicene and $\mathrm{MoS}_2$, and comparison made with other known results.

cond-mat.mes-hall↗

arXiv2015

Generalized fluctuation theorems for classical systems

Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of the work $p(W)/p(-W)=\exp(αW)$. We derive the general form of the fluctuation theorems for an arbitrary Gaussian Markov process and find conditions when the parameter $α$ becomes a universal parameter $1/kT$. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is non-trivial. The generalized theorems are equally valid for non-equilibrium steady states.

physics.class-ph↗

arXiv2012

Partial decoherence in mesoscopic systems

The coupling of a mesoscopic system with its environment usually causes total decoherence: at long times the reduced density matrix of the system evolves in time to a limit which is independent of its initial value, losing all the quantum information stored in its initial state. Under special circumstances, a subspace of the system's Hilbert space remains coherent, or "decoherence free", and the reduced density matrix approaches a non-trivial limit which contains information on its initial quantum state, despite the coupling to the environment. This situation is called "partial decoherence". Here we find the conditions for partial decoherence for a mesoscopic system (with $N$ quantum states) which is coupled to an environment. When the Hamiltonian of the system commutes with the total Hamiltonian, one has "adiabatic decoherence", which yields N-1 time-independent combinations of the reduced density matrix elements. In the presence of a magnetic flux, one can measure circulating currents around loops in the system even at long times, and use them to retrieve information on the initial state. For N=2, we demonstrate that partial decoherence can happen only under adiabatic decoherence conditions. However, for $N>2$ we find partial decoherence even when the Hamiltonian of the system does not commute with the total Hamiltonian, and we obtain the general conditions for such non-adiabatic partial decoherence. For an electron moving on a ring, with $N>2$ single-level quantum dots, non-adiabatic partial decoherence can arise only when the total flux through the ring vanishes (or equals an integer number of flux quanta), and therefore there is no asymptotic circulating current.

cond-mat.mes-hall↗