arXiv subjects

Bijay Kumar Agarwalla

Publications and source records attributed to Bijay Kumar Agarwalla.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain

We investigate the dynamics of full counting statistics (FCS) of the growth of the total number of fermions in a one-dimensional non-interacting lattice subjected to a localized particle gain (source) at one edge. The dynamics of the setup is modeled by the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) quantum master equation. We recast the counting problem that involves counting particle number at every lattice site to a problem where only the local injected site is involved. We employ the Schwinger-Keldysh path integral formalism within the GKSL framework and derive an analytical expression for the cumulant generating function at arbitrary times and obtain a Levitov-Lesovik type formula in the long-time limit, earlier derived for boundary driven setups in the steady-state. For clean lattices with either short- or long-range hopping, supporting single-particle delocalized eigenstates, we show that all cumulants grow linearly with time in the asymptotic regime. Our analytical results are in excellent agreement with direct numerical simulations. These findings establish a general framework for characterizing FCS and quantum fluctuations in driven open fermionic systems with localized particle injection.

cond-mat.stat-mech↗

arXiv2026

Symmetry structure dependent diagnostic of the Quantum Mpemba Effect

Understanding symmetry restoration in isolated quantum many-body systems is an important problem in nonequilibrium many-body quantum physics. Recent studies have shown that the quantum Mpemba effect can be characterized through entanglement asymmetry, where states with stronger initial symmetry breaking restore symmetry faster. However, it remains unclear whether conventional energy-based measures, such as the trace distance, capture the same phenomenon. We investigate this question in closed spin-$1/2$ quantum systems with different symmetries by analyzing the dynamics of symmetry-breaking initial states. Combining numerical simulations with an analytical decomposition of the trace distance into symmetry-coherence and residual contributions, we identify the conditions under which trace distance tracks entanglement asymmetry and reproduces the Mpemba--like behavior observed in it. For charge symmetry, the residual contribution is negligible, making the trace distance effectively governed by symmetry-sector coherences. In contrast, for permutation symmetry, a significant residual contribution leads to qualitatively different relaxation dynamics. Our results establish when conventional energy-based diagnostics reliably capture symmetry-restoration dynamics and clarify the distinct physical information encoded by entanglement asymmetry and trace distance.

quant-ph↗

arXiv2026

Long-time Dynamics of Many-body Open Quantum Systems using Quantum Generating Functions

The interplay between coherent unitary evolution and environment-induced dissipation can give rise to a wide range of non-equilibrium dynamics in open quantum systems, ranging from interesting transport phenomena to dynamical phase transitions. However, accessing such long-time dynamics remains challenging for the existing methods developed for the simulation of many-body open quantum systems. We address this problem by developing a quantum generating function (QGF) formalism for open many-body systems for both ensemble-averaged dynamics governed by a Markovian quantum master equation and trajectory-resolved dynamics described by the quantum trajectory formalism, including quantum jumps, and quantum state diffusion. Our approach computes the dynamics of higher-order moments and fluctuation statistics without explicitly evolving the quantum state, thereby providing an efficient and scalable approach for investigating many-body open quantum systems. We demonstrate the versatility of the formalism by applying it to both the integrable open XXZ chain and the nonintegrable open next-nearest-neighbor XXZ spin chain, where it uncovers distinct initial state dependent long-time transport regimes. Our work establishes quantum generating functions as an efficient and scalable framework for investigating long-time dynamics in open quantum many-body systems.

cond-mat.stat-mech↗

arXiv2026

Beyond-ballistic transport in an open quantum ring

In an open quantum ring (OQR), an asymmetric ring-to-electrode configuration, where the upper and lower arms have unequal lengths, generates antiresonances in the junction transmission spectrum around the doubly degenerate eigenenergies of the isolated ring Hamiltonian. The asymmetric OQR also gives rise to a net circular current transmission within the ring, specifically around these doubly degenerate eigenenergies. We investigate the system-size scaling properties of the transmission within the ring and the overall junction transmission of an OQR. Ballistic transport refers to the unhindered flow of charge carriers within a conductor, where transmission is independent of the system size. Here, we find beyond-ballistic behavior, characterized by an anomalous increase of the transmission with increasing system size, near both the degenerate and non-degenerate eigenenergies of the ring Hamiltonian, depending on the ring-to-electrode configuration. This phenomenon is unique to OQRs and is associated with the quantum interference effect between two counter-propagating electronic waves with nearly equal and opposite momenta. Consequently, there is no equivalent phenomenon in open quantum junctions with linear conductors.

cond-mat.mes-hall↗

arXiv2026

Quantum Mpemba effect for operators in open systems

The quantum Mpemba effect concerns with anomalous relaxation of quantum states that evolves either under unitary or non-unitary dynamics. In the context of open quantum systems, while most studies focus on quantum states evolving under completely positive trace-presing dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we demonstrate that an analogous effect can arise at the level of operators. In particular, we show that operators that evolves under the adjoint Liouvillian -- despite not being a trace-preserving map -- can still exhibit a genuine Mpemba effect. We derive general conditions under which this phenomenon can occur and validate our predictions for three different open quantum setups. Our results broaden the scope of the Mpemba effect in quantum systems and provide a framework for controlling the relaxation of physically relevant observables.

cond-mat.stat-mech↗

arXiv2026

Principal component analysis of wavefunction snapshots in non-equilibrium dynamics

We study non-equilibrium quantum dynamics by performing principal component analysis on the data sets of wavefunction snapshots. We show that a specific transformation of the data sets maximizes the information content in the largest principal component and further enables its connection to certain observables. This connection enables us to explain the dynamical features revealed by such a dimensionality-reduction scheme. We demonstrate this using quantum dynamics of the Heisenberg spin chain, starting from different initial states, and further extend the approach to extract higher-order correlations. Our framework should also be applicable to other unsupervised machine-learning methods based on dimensionality-reduction schemes and is highly relevant to experiments with quantum simulators, including those in higher dimensions.

cond-mat.stat-mech↗

arXiv2026

Measurement induced faster symmetry restoration in quantum trajectories

Continuous measurement of quantum systems provides a standard route to quantum trajectories through the successive acquisition of information which further results in measurement back-action. In this work, we harness this back-action as a resource for global $U(1)$ symmetry restoration where continuous measurement is combined with a $U(1)$-preserving unitary evolution. Starting from a $U(1)$ symmetry-broken initial state, we simulate quantum trajectories generated by continuous measurements of both global and local observables. We show that under global monitoring, states containing superpositions of distant charge sectors restore symmetry faster than those involving nearby sectors. We establish the universality of this behavior across different measurement protocols. Finally, we demonstrate that local monitoring can further accelerate symmetry restoration for certain states that relax slowly under global monitoring.

cond-mat.stat-mech↗

arXiv2025

Detection of Mpemba effect through good observables in open quantum systems

The Mpemba effect refers to the anomalous relaxation of a quantum state that, despite being initially farther from equilibrium, relaxes faster than a closer counterpart. Detecting such a quantum Mpemba effect typically requires full knowledge of the quantum state during its time evolution, which is an experimentally challenging task since state tomography becomes exponentially difficult as system size increases. This poses a significant obstacle in studying Mpemba effect in complex many-body systems. In this work, we demonstrate that this limitation can be overcome by identifying suitable observables that signal rapid relaxation. Moreover, as long as the system equilibrates to a known unique steady-state, it is possible to fully detect the occurrence of quantum Mpemba effect just by measuring the observable for known state preparations. Our approach thus significantly reduces experimental complexity and offers a practical route for observing the quantum Mpemba effect in complex and extended multi-qubit setups.

cond-mat.stat-mech↗

arXiv2025

Full counting statistics for boundary driven transport in presence of correlated gain and loss channels

One of the major advances of quantum technology is the engineering of complex quantum channels in lattice systems that paves the way for a variety of novel non-equilibrium phenomena. For a boundary driven lattice with such engineered quantum channels, the analysis of the full counting statistics of current across boundaries has received limited attention. In this work, we consider a boundary driven free fermionic lattice with carefully engineered correlated gain and loss channels and obtain the cumulant generating function of the steady-state particle current. We also discuss the limit for simplifying the correlated gain-loss channel to a local gain-loss channel and obtain the average current and its fluctuation in such cases. Generally, in the presence of gain-loss, the current statistics are different at the two ends of the lattice. Hence, for both local and correlated gain-loss, we devise the conditions for which the statistics can coincide, giving rise to a $\mathcal{PT}$ symmetric balanced gain-loss scenario. A striking difference between the correlated gain-loss and their local counterpart is the emergence of nonreciprocity in the system and we observe that it has a dramatic impact in the current as well as fluctuations. Our work therefore provides interesting insights about the importance of engineered dissipators in boundary driven systems.

cond-mat.stat-mech↗

arXiv2025

Dynamics of number entropy for free fermionic systems in presence of defects and stochastic processes

We investigate the dynamics of number entropy in a chain of free fermions subjected to both defects and stochastic processes. For a special class of defects, namely conformal defects, we present analytical and numerical results for the temporal growth of number entropy, the time evolution of the number distribution, and the eigenvalue profile of the associated correlation matrix within a subsystem. We show that the number entropy exhibits logarithmic growth in time, originating from the Gaussian structure of the number distribution. We find that the eigenvalue dynamics reveal a profound connection to the reflection and transmission coefficients of the associated scattering problem for a broad range of defects. When stochastic processes are introduced, specifically Stochastic Unitary Processes (SUP) and Quantum State Diffusion (QSD), the number entropy scales as $\ln(t)$ in the SUP case and shows strong hints of $\ln [\ln(t)]$ scaling in the QSD case. These findings establish compelling evidence that number entropy grows logarithmically slower than the corresponding von Neumann entanglement entropy across a wide class of systems.

quant-ph↗

arXiv2025

Quantum dynamics in lattices in presence of bulk dephasing and a localized source

The aim of this work is to study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing. We consider two classes of one-dimensional lattice systems: (i) a non-interacting lattice with nearest-neighbor and beyond, i.e., long-ranged (power-law) hopping, and (ii) a lattice that is interacting via short-range interactions modeled by a fermionic quartic Hamiltonian. We study the evolution of the local density profile $n_i(t)$ within the system and the growth of the total particle number $N(t)$ in it. For case (i), we provide analytical insights into the dynamics of the nearest-neighbor model using an adiabatic approximation, which relies on assuming faster relaxation of coherences of the single particle density matrix. For case (ii), we perform numerical computations using the time-evolving block decimation (TEBD) algorithm and analyze the density profile and the growth exponent in $N(t)$. Our detailed study reveals an interesting interplay between Hamiltonian dynamics and various environmentally induced mechanisms in open quantum systems, such as local source and bulk dephasing. It brings out rich dynamics, including universal dynamical scaling and anomalous behavior across various time scales and is of relevance to various quantum simulation platforms.

quant-ph↗

arXiv2025

Accelerated relaxation and Mpemba-like effect for operators in open quantum systems

Quantum Mpemba effect occurs when a quantum system, residing far away from the steady state, relaxes faster than a relatively nearer state. We look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a non-trace preserving map, the trace distance of an operator is not a monotonically decaying function of time, unlike its quantum state counterpart. Consequently, the trace distance can not serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a \textit{dressed} distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. Applying the formalism to various open quantum system settings, we find that, interestingly, in the single qubit case, only accelerated relaxation of operators is possible, while genuine Mpemba-like effects emerge in higher-dimensional systems such as qutrits and beyond. Furthermore, we demonstrate the existence of Mpemba-like effects in nonlocal, non-equilibrium operators, such as current, in a double-quantum-dot setup. Our results, besides offering fundamental insight about the occurrence of the Mpemba-like effect under non-trace preserving dynamics, open avenues for new experimental studies where quicker relaxation of observables could be of significant interest.

cond-mat.stat-mech↗

arXiv2025

Enhancing the Performances of Autonomous Quantum Refrigerators via Two-Photon Transitions

Conventional autonomous quantum refrigerators rely on uncorrelated heat exchange between the working system and baths via two-body interactions enabled by single-photon transitions and positive-temperature work baths, inherently limiting their cooling performance. Here, we introduce distinct qutrit refrigerators that exploit correlated heat transfer via two-photon transitions with the hot and cold baths, yielding a genuine enhancement in performance over conventional qutrit refrigerators that employ uncorrelated heat transfer. These refrigerators achieve at least a twofold enhancement in cooling power and reliability compared to conventional counterparts. Moreover, we show that cooling power and reliability can be further enhanced simultaneously by several folds, even surpassing existing cooling limits, by utilizing a synthetic negative-temperature work bath. Such refrigerators can be realized by combining correlated heat transfer and synthetic work baths, which consist of a four-level system coupled to hot and cold baths and two conventional work baths via two independent two-photon transitions. Here, the composition of two work baths effectively creates a synthetic negative-temperature work bath under suitable parameter choices. Additionally, our autonomous refrigerators with negative temperature baths significantly outperform previously studied autonomous and non-autonomous refrigerators in terms of cooling ability without requiring any additional energy resources, as they cool the cold bath to much lower temperature, which is forbidden for others refrigerators. Our results demonstrate that correlated heat transfers and baths with negative temperatures can yield thermodynamic advantages in quantum devices. Finally, we discuss the experimental feasibility of the proposed refrigerators across various existing platforms.

quant-ph↗

arXiv2025

Emergence of distinct relaxation behaviour and Quantum Regression Theorem in the Ultra-strong Coupling Limit

In the framework of open quantum systems, we derive the dynamical equation governing two-time correlation functions in the ultra-strong coupling (USC) regime between the system and its environment. Unlike the case of the standard weak-coupling regime, in the USC case, we find distinct relaxation behavior for two-time correlators depending on the types of the operators involved in the correlation function. Interestingly, the Quantum Regression Theorem (QRT) emerges after the fastest relaxation time-scale, which is governed by the system-bath coupling strength. We exemplify our findings for the dissipative spin-boson model and further find excellent agreement with the numerically exact hierarchical equations of motion (HEOM) method.

cond-mat.stat-mech↗

arXiv2025

Thermoelectric performance of a minimally nonlinear voltage probe and voltage-temperature probe heat engine with broken time-reversal symmetry

We investigate the thermoelectric performance of minimally nonlinear irreversible heat engines with broken time-reversal symmetry (TRS), realized through voltage and voltage-temperature probe configurations. Our framework extends the Onsager relations by incorporating a nonlinear power dissipation term into the heat current. We derive and analyze analytical expressions for the efficiency at a given power and the efficiency at maximum power (EMP), expressed in terms of asymmetry parameters and generalized figures of merit. Our analysis reveals that the combined effects of broken TRS and nonlinear dissipation give rise to two universal bounds on the EMP that can surpass the Curzon-Ahlborn (CA) limit. Although these bounds share a similar analytical form, differences in Carnot efficiency and asymmetry parameters lead to distinct operational characteristics, as shown through numerical simulations. We consider a triple-quantum-dot Aharonov-Bohm heat engine incorporating either a voltage probe or a voltage-temperature probe. In both cases, TRS is broken by the magnetic flux. However, the voltage-temperature probe requires an additional anisotropy in the system for its TRS-breaking effects to significantly influence transport. We examine the role of this anisotropy in enhancing performance. Our results show that the EMP and efficiency at a given power can be enhanced by increasing the strength of nonlinear power dissipation, even though the output power remains unchanged. The voltage probe configuration generally yields higher power, while the voltage-temperature probe is more efficient, except in certain regimes where large asymmetries and high figures of merit allow the voltage probe setup to outperform.

cond-mat.mes-hall↗

arXiv2025

Understanding synchronization between quantum self-sustained oscillators through coherence generation

Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable oscillators, between two arbitrary quantum spins, and within a hybrid setup involving a spin and an oscillator. We derive a simple and general condition on the elements of the joint density matrix that must be satisfied for them to contribute to the relative phase distribution. In particular, we identify the subset of coherence elements in the joint density matrix that serve as key resources for enabling quantum phase synchronization. Our theory is validated against the previously proposed interaction models known to induce synchronization between the self-sustained oscillators. Moreover, our approach offers valuable insights into the relationship between phase synchronization and various information-theoretic measures.

quant-ph↗

arXiv2025

Bipartite particle number fluctuations in dephased long-range lattice systems

We investigate the dynamics of subsystem particle number fluctuations in a long-range system with power-law decaying hopping strength characterized by exponent $μ$ and subjected to a local dephasing at every site. We introduce an efficient {\it bond length} representation for the four-point correlator, enabling the large-scale simulation of the dynamics of particle number fluctuations from translationally invariant initial states. Our results show that the particle number fluctuation dynamics exhibit one-parameter Family-Vicsek scaling, with superdiffusive scaling exponents for $μ< 1.5$ and diffusive scaling exponents for $μ\geq 1.5$. Finally, exploiting the bond-length representation, we provide an exact analytical expression for the particle number fluctuations and their scaling exponents in the short-range limit ($μ\to \infty)$.

cond-mat.stat-mech↗

arXiv2025

Assessment of spectral phases of non-Hermitian quantum systems through complex and singular values

Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective measure to study dissipative quantum chaos. Motivated by the rich properties of non-Hermitian power-law banded random matrices and its promise as a platform to study localized and delocalized phases in non-Hermitian systems, we make an in-depth study to assess different spectral phases of these matrices through the lens of both complex eigenvalues and singular values. Remarkably, the results from complex spectra and singular value analysis are seemingly different, thereby necessitating caution while identifying different phases. We also exemplify our findings by studying a non-Hermitian Hamiltonian with a complex on-site disorder. Our work indicates that systems, where disorder is present both in the Hermitian and non-Hermitian segments of a Hamiltonian, are sensitive to the specific diagnostic tool that needs to be employed to study quantum chaos.

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