arXiv subjects

Sourabh Lahiri

Publications and source records attributed to Sourabh Lahiri.

At least 19 recordsLinked to original sources

arXiv2026

Quantum synchronization: A tutorial guide

Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.

quant-ph↗

arXiv2025

Two and three-state quantum heat engines with stochastic resetting

Quantum heat engines have undergone extensive studies over the last two decades. Simultaneously, the studies of the applications of stochastic resetting in various fields are on the rise. We explore the effect of stochastic resetting on the dynamics of a two-level and a three-level quantum heat engine. The extracted work is shown to increase with the resetting rate. The effective efficiency that takes into account the work done due to resetting remains constant. However, if the work done due to resetting is ignored, then the system can incorrectly imply a different behaviour, including the false inference that it is not working as an engine at all. The efficient power is observed to increase beyond that obtained in the absence of resetting, and is shown to be higher for a three-level engine.

cond-mat.stat-mech↗

arXiv2025

Micro Heat Engines With Hydrodynamic Flow

Hydrodynamic flows are often generated in colloidal suspensions. Since colloidal particles are frequently used to construct stochastic heat engines, we study how the hydrodynamic flows influence the output parameters of the engine. We study a single colloidal particle confined in a harmonic trap with time-periodic stiffness that provides the engine protocol, in presence of a steady linear shear flow. The nature of the flow (circular, elliptic or hyperbolic) is externally tunable. At long times, the work done by the flow field is shown to dominate over the thermodynamic (Jarzynski) work done by the trap, if there is an appreciable deviation from the circular flow. The work by the time dependent trap is the sole contributor only for a perfectly circular flow. We also study an extended model, where a microscopic spinning particle (spinor) is tethered close to the colloidal particle, i.e. the working substance of the engine, such that the flow generated by the spinor influences the dynamics of the colloidal particle. We simulate the system and explore the influence of such a flow on the thermodynamics of the engine. We further find that for larger spinning frequencies, the work done by the flow dominates and the system cannot produce thermodynamic work.

cond-mat.stat-mech↗

arXiv2024

Two-dimensional ASEP model to study density profiles in CVD growth

The growth of two-dimensional (2D) transition metal dichalcogenides using chemical vapor deposition has been an area of intense study, primarily due to the scalability requirements for potential device applications. One of the major challenges of such growths is the large-scale thickness variation of the grown film. To investigate the role of different growth parameters computationally, we use a 2D asymmetric simple-exclusion process (ASEP) model with open boundaries as an approximation to the dynamics of deposition on the coarse-grained lattice. The variations in concentration of particles (growth profiles) at the lattice sites in the grown film are studied as functions of parameters like injection and ejection rate of particles from the lattice, time of observation, and the right bias (difference between the hopping probabilities towards right and towards left) imposed by the carrier gas. In addition, the deposition rates at a given coarse-grained site is assumed to depend on the occupancy of that site. The effect of the maximum deposition rate, i.e., the deposition rate at a completely unoccupied site on the substrate, has been explored. The growth profiles stretch horizontally when either the evolution time or the right bias is increased. An increased deposition rate leads to a step-like profile, with the higher density region close to the left edge. In 3D, the growth profiles become more uniform with the increase in the height of the precursor with respect to the substrate surface. These results qualitatively agree with the experimental observations.

cond-mat.stat-mech↗

arXiv2024

Efficiency of a microscopic heat engine subjected to stochastic resetting

We explore the thermodynamics of stochastic heat engines in presence of stochastic resetting. The set-up comprises an engine whose working substance is a Brownian particle undergoing overdamped Langevin dynamics in a harmonic potential with a time-dependent stiffness, with the dynamics interrupted at random times with a resetting to a fixed location. The effect of resetting to the potential minimum is shown to enhance the efficiency of the engine, while the output work is shown to have a non-monotonic dependence on the rate of resetting. The resetting events are found to drive the system out of linear response regime even for small differences in the bath temperatures. Shifting the reset point from the potential minimum is observed to reduce the engine efficiency. The experimental set-up for the realization of such an engine is briefly discussed.

cond-mat.stat-mech↗

arXiv2023

Exploring outputs from concatenated stochastic heat engines

Recent works on the concatenation of two simple heat engines have shown that it may lead to non-monotonic variations in the efficiency and power with parameters like driving amplitudes and asymmetries in cycle periods. Motivated by this study, we investigate the effect of the concatenation between two stochastic heat engines where colloidal particles have been trapped in harmonic potentials. The stiffness parameters of each engine are varied cyclically, but with different cycle periods, with a common thermal bath that acts as a sink for the first engine but as a source for the second. We consider two types of protocols, first where the trap strength undergoes sudden jumps, and the second where it varies linearly with time. In both we find several non-trivial effects, like the the non-monotonic functional dependence of the engine outputs on several parameters used in the setup. For a protocol that varies linearly with time, the concatenation leads to enhanced output power as compared to a single effective engine, in a suitable range of parameters. It has been shown that the output from the combined system shows a peak with respect to the asymmetry in cycle times of the engines that have been concatenated. A general relation of the efficiency of an arbitrary number of concatenated engines driven quasistatically has been provided.

cond-mat.stat-mech↗

arXiv2023

Thermodynamics of one and two-qubit quantum refrigerators interacting with squeezed baths: a comparative study

We investigate the nonequilibrium refrigeration of one and two-qubit systems in a squeezed thermal bath. We characterize the performance of one and two-qubit refrigerators in the presence of squeezed heat baths, in terms of their coefficients of performance, cooling rates, and figures of merit. Our results show that the performance of the refrigerators is strongly influenced by the squeezing parameter and the number of qubits. The performance of the two-qubit refrigerator is found to be better than that of the one-qubit refrigerator under the same operating conditions. Our findings suggest that a squeezed thermal bath can be a promising resource for the design of efficient quantum refrigerators in the non-equilibrium regime.

cond-mat.stat-mech↗

arXiv2023

Stochastic Heat Engine Using Multiple Interacting Active Particles

The area of stochastic heat engines using active particles has attracted a lot of attention recently. They have been shown to exhibit advantages over engines using passive particles. In this work, we use multiple self-propelling particles undergoing Vicsek-like aligning interaction as our working system. The particles are confined in a two-dimensional circular trap. The interplay between the confinement and the activity of the particles induces clustering. These clusters change their locations relative to the walls of the trap, when the wall steepness is varied with time. In this work we demonstrate that changing the steepness of the wall and the activity of the particles time-periodically can cause the system to act as an engine. In this setup, we study the variations in extracted work with the activity, rotational diffusion, and the Vicsek radius of individual particles. We also comment on the complications involved in the definition of the engine efficiency in accordance with the usual prescription of stochastic thermodynamics.

cond-mat.stat-mech↗

arXiv2022

Thermodynamics of one and two-qubit nonequilibrium heat engines running between squeezed thermal reservoirs

Quantum heat engines form an active field of research due to their potential applications. There are several phenomena that are unique to the quantum regime, some of which are known to give these engines an edge over their classical counterparts. In this work, we focus on the study of one and two-qubit finite-time Otto engines interacting with squeezed thermal baths, and discuss their important distinctions as well as the advantage of using the two-qubit engine. In particular, the two-qubit engine offers an interesting study of the interplay between the degree of squeezing and that of the coherence between the two qubits. We find that the two-qubit engine generally yields higher power than its one-qubit counterpart. The effective temperature of the squeezed baths can be calculated both for the one and two-qubit engines, and they tend to show an exponential growth with increase in squeezing parameters $r_h$ and $r_c$. It is also observed that by tuning the squeezing parameters, the machine can be made to work either in the engine or in the refrigerator mode. Additional effects due to the change in the inter-qubit separation have been studied.

cond-mat.stat-mech↗

arXiv2021

Microscopic thermal machines using run-and-tumble particles

Microscopic thermal machines that are of the dimensions of around few hundred nanometers have been the subject of intense study over the last two decades. Recently, it has been shown that the efficiency of such thermal engines can be enhanced by using active Ornstein-Uhlenbeck particles (AOUP). In this work, we numerically study the behaviour of tiny engines and refrigerators that use an active run-and-tumble particle (RTP) as the working system. We find that the results for the engine mode are in sharp contrast with those of engines using AOUP, thus showing that the nature of activity has a strong influence on the qualitative behaviours of thermal machines for nonequilibrium cycles. The efficiency of an engine using a run-and-tumble particle is found to be smaller in general than a passive microscopic engine. However, when the applied protocol is time-reversed, the resulting microscopic refrigerator can have a much higher coefficient of performance under these conditions. The effect of variation of different parameters of the coefficient of performance has been explored. A non-monotonic variation of coefficient of performance with active force has been found.

cond-mat.stat-mech↗

arXiv2020

Exploring the extent of validity of quantum work fluctuation theorems in the presence of weak measurements

Quantum work fluctuation theorems are known to hold when the work is defined as the difference between the outcomes of projective measurements carried out on the Hamiltonian of the system at the initial and the final time instants of the experimental realization of the process. A recent study showed that the theorem breaks down if the measurement is of a more general nature, i.e. if a positive operator valued measurement is used, and the deviation vanishes only in the limit where the operators become projective in nature. We study a simple two-state system subjected to a unitary evolution under a Hamiltonian that is linearly dependent on time, and verify the validity of the above statement. We further define a weak value of work and show that the deviation from the exact work fluctuation theorems are much less in this formalism.

cond-mat.stat-mech↗

arXiv2019

A stochastic heat engine using an active particle

The topic of microscopic heat engine has undergone intensive research in recent years. Microscopic heat engines can exploit thermal as well as active fluctuations to extract thermodynamic work. We investigate the properties of a microscopic Stirling's engine that uses an active (self-propelling) particle as a working substance, in contact with two thermal baths. It is shown that the presence of activity leads to an enhanced performance of the engine. The efficiency can be improved by increasing the activity strength for all cycle time, including the non-quasistatic regime. We verify that the analytical results agree very well with our simulations. The variation of efficiency with the temperature difference between the two thermal baths has also been explored. The optimum region of operation of the engine has been deduced, by using its efficient power as a quantifier. Finally, a simple model is provided that emulates the behaviour of a flywheel driven by this engine.

cond-mat.stat-mech↗

arXiv2019

Stochastic energetics and thermodynamics at small scales

At very small scales, thermodynamic energy exchanges like work and heat become comparable to thermal energy of the system, which leads to unusual phenomena like the transient violations of Second Law. We explore the generic characters of such systems using the framework of Stochastic Thermodynamics and provide a preliminary overview of the basic concepts. Here we have attempted to put into simple terms some actively pursued topics like the arrow of time, effect of information gain on Second Law, explanation of origin of life using Crooks theorem and the thermodynamic uncertainty relations.

cond-mat.stat-mech↗

arXiv2019

Convergence of thermodynamic quantities and work fluctuation theorems in presence of random protocols

Recently many results namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of equilibrium by an external time-dependent parameter which follows a particular {\it protocol}. One needs to perform several iterations of the same experiment in order to find statistically relevant results. Since the systems are microscopic, fluctuations dominate. Studying the convergence of relevant thermodynamics quantities with number of realizations is also important as it gives a rough estimate of number of iterations one needs to perform. In each iteration the protocol follows a predetermined {\it identical/fixed} form. However, the protocol itself may be prone to fluctuations. In this work we are interested in looking at a simple non-equilibrium system namely a Brownian particle trapped in a harmonic potential. The center of the trap is then dragged according to a protocol. We however lift the condition of fixed protocol. In our case the protocol in each realization is different. We consider one of the parameters of the protocol as a random variable, chosen from some known distribution. We study the systems analytically as well as numerically. We specifically study the convergence of the average work and free energy difference with number of realizations. Interestingly, in several cases, randomness in the protocol does not seem to affect the convergence when compared to fixed protocol results. We study symmetry functions. A Brownian particle in a double well potential is also studied numerically. We believe that our results can be experimentally verified.

cond-mat.stat-mech↗

arXiv2018

Return to origin problem for particle on a one-dimensional lattice with quasi-Zeno dynamics

In recent work, the so-called quasi-Zeno dynamics of a system has been investigated in the context of the quantum first passage problem. This dynamics considers the time evolution of a system subjected to a sequence of selective projective measurements made at small but finite intervals of time. This means that one has a sequence of steps, with each step consisting of a unitary transformation followed by a projection. The dynamics is non-unitary and, in recent work, it has been shown that it can be effectively described by two different non-Hermitian Hamiltonians. Here we explore this connection by considering the problem of detecting a free quantum particle moving on a one-dimensional lattice, where the detector is placed at the origin and the particle is initially located at some specified lattice point. We find that results for distribution times for the first detection probability, obtained from the non-Hermitian Hamiltonians, are in excellent agreement with known exact results as well as exact numerics. Interesting finite-size effects are discussed. We also study the first detection problem for the example of a particle moving in a quasi-periodic potential, an example where the unperturbed particle's motion can be ballistic, localized or diffusive.

quant-ph↗

arXiv2017

Information-theoretic analysis of the directional influence between cellular processes

Inferring the directionality of interactions between cellular processes is a major challenge in systems biology. Time-lagged correlations allow to discriminate between alternative models, but they still rely on assumed underlying interactions. Here, we use the transfer entropy (TE), an information-theoretic quantity that quantifies the directional influence between fluctuating variables in a model-free way. We present a theoretical approach to compute the transfer entropy, even when the noise has an extrinsic component or in the presence of feedback. We re-analyze the experimental data from Kiviet et al. (2014) where fluctuations in gene expression of metabolic enzymes and growth rate have been measured in single cells of E. coli. We confirm the formerly detected modes between growth and gene expression, while prescribing more stringent conditions on the structure of noise sources. We furthermore point out practical requirements in terms of length of time series and sampling time which must be satisfied in order to infer optimally transfer entropy from times series of fluctuations.

q-bio.QM↗

arXiv2017

Generalized Second Law and optimal protocols for nonequilibrium systems

A generalized version of the Maximum Work Theorem is valid when the system is initially not at thermal equilibrium. In this work, we initially study the fraction of trajectories that violate this generalized theorem for a two simple systems: a particle in a harmonic trap (i) whose centre is dragged with some protocol, and (ii) whose stiffness constant changes as a function of time. We also find the optimal protocol that minimizes the average change in total entropy. To our surprise, we find that optimization of protocol does not necessarily entail maximum violation fraction.

cond-mat.stat-mech↗

arXiv2017

Nonequilibrium steady states in Langevin thermal systems

Equilibrium is characterized by its fundamental properties such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuation-dissipation relation mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocity-dependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.

cond-mat.stat-mech↗