arXiv subjects

Archak Purkayastha

Publications and source records attributed to Archak Purkayastha.

At least 19 recordsLinked to original sources

arXiv2026

Quantum non-Markovian Hatano-Nelson model

While considering non-Hermitian Hamiltonians arising in the presence of dissipation, in most cases, the dissipation is taken to be frequency independent. However, this idealization may not always be applicable in experimental settings, where dissipation can be frequency-dependent. Such frequency-dependent dissipation leads to non-Markovian behavior. In this work, we demonstrate how a quantum non-Markovian Hatano-Nelson model arises microscopically in a quasi-one-dimensional dissipative lattice. This is achieved using non-equilibrium Green's functions without requiring any approximation like weak system-bath coupling or a time-scale separation, which would have been necessary for a Markovian treatment. The resulting effective system exhibits nonreciprocal hopping, the defining characteristic of the Hatano-Nelson model, as well as uniform dissipation, both of which are frequency-dependent. This holds for both bosonic and fermionic settings. We find solely non-Markovian nonreciprocal features like unidirectional frequency blocking in bosonic settings, and a particular type of non-equilibrium dissipative quantum phase transition in fermionic settings, that cannot be captured in a Markovian theory, nor have any analog in reciprocal systems. Our results lay the groundwork for describing and engineering non-Markovian nonreciprocal quantum lattices.

quant-ph↗

arXiv2026

Semidefinite programming for understanding the limitations of Lindblad equations

Lindbladian quantum master equations (LEs) are the most popular descriptions for quantum systems weakly coupled to baths. But, recent works have established that in many situations such Markovian descriptions are fundamentally limited: they cannot simultaneously capture populations and coherences even to the leading-order in system-bath couplings. This can cause violation of fundamental properties like thermalization and continuity equations associated with local conservation laws, even when such properties are expected in the actual setting. This begs the question: given a physical situation, how do we know if there exists an LE that describes it to a desired accuracy? Here we show that, for both equilibrium and non-equilibrium steady states (NESS), this question can be succinctly formulated as a semidefinite program (SDP), a convex optimization technique. If a solution to the SDP can be found to a desired accuracy, then an LE description is possible for the chosen setting. If not, no LE description is fundamentally attainable, showing that a consistent Markovian treatment is impossible even at weak system-bath coupling for that particular setting. Considering few qubit isotropic XXZ-type models coupled to multiple baths, we find that in most parameter regimes, LE description giving accurate populations and coherences to leading-order is unattainable, leading to rigorous no-go results. However, in some cases, LE description having correct populations but inaccurate coherences, and satisfying local conservation laws, is possible over some of the parameter regimes. Our work highlights the power of semidefinite programming in the analysis of physically consistent LEs, thereby, in understanding the limits of Markovian descriptions at weak system-bath couplings.

quant-ph↗

arXiv2025

Accelerated calculation of impurity Green's functions exploiting the extreme Mpemba effect

Simulating the dynamics of quantum impurity models remains a fundamental challenge due to the complex memory effects that arise from system-environment interactions. Of particular interest are two-time correlation functions of an impurity, which are central to the characterization of these many-body systems, and are a cornerstone of the description of correlated materials in dynamical mean field theory (DMFT). In this work, we extend our previous work on the extrapolation of single-time observables to demonstrate an efficient scheme for computing two-time impurity correlation functions, by combining the non-Markovian quantum Mpemba effect (NMQMpE) with a dynamical map-based framework for open quantum systems. Our method is benchmarked against exact and known accurate results in prototypical impurity models for both fermionic and bosonic environments, demonstrating significant computational savings compared to state-of-the-art methods.

quant-ph↗

arXiv2025

On the difference between thermalization in open and isolated quantum systems: a case study

Thermalization of isolated and open quantum systems has been studied extensively. However, being the subject of investigation by different scientific communities and being analysed using different mathematical tools, the connection between the isolated (IQS) and open (OQS) approaches to thermalization has remained opaque. Here we demonstrate that the fundamental difference between the two paradigms is the order in which the long time and the thermodynamic limits are taken. This difference implies that they describe physics on widely different time and length scales. Our analysis is carried out numerically for the case of a double quantum dot (DQD) coupled to a fermionic lead, also known as the interacting resonant level model in quantum impurity physics. We show how both OQS and IQS thermalization can be explored in this model on equal footing, allowing a fair comparison between the two. We find that while the quadratically coupled (free) DQD experiences no isolated thermalization, it of course does experience open thermalization. For the non-linearly interacting DQD coupled to a fermionic lead, the many-body interaction in the DQD breaks the integrability of the whole system. We find that this system shows strong evidence of both OQS and IQS thermalization in the same dynamics, but at widely different time scales, consistent with reversing the order of the long time and the thermodynamic limits.

cond-mat.mes-hall↗

arXiv2025

Quantum many-body attractors

Complex dynamics when occurring autonomously, i.e. without external driving, is usually associated with everyday length scales and classical physics, e.g. living organisms. This dynamics is \emph{not} quantum coherent. Quantum coherent dynamics is, by contrast, assumed to be either simple periodic oscillation in particular when autonomous, e.g. spin precession, or random quantum fluctuations. Combining autonomous complex and quantum coherent dynamics on microscopic length-scales could allow for novel coherent quantum machines working without external time-dependent driving. Motivated by this, here we provide an exact theoretical condition for a system to display complex quantum coherent dynamics on both microscopic and macroscopic length scales that we call a \emph{dynamical quantum algebraic thread} (D-QAT). Due to D-QATs our autonomous quantum coherent dynamics is robust to realistic imperfections (including low-doped disorder) and present for generic initial states, allowing for potential realisations in experiments. We give an example of a \emph{spin lace} model structurally similar to magnetic azurite and certain recently experimentally realized large single-molecular magnets with long coherence times. Our work opens the possibility for many potential applications including ultra-dense storage and manipulation of quantum memories, creating \emph{giant} quantum coherent qubits, or microscopic quantum mechanism perform complicated motion.

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arXiv2024

Extracting Dynamical Maps of Non-Markovian Open Quantum Systems

The most general description of quantum evolution up to a time $τ$ is a completely positive tracing preserving map known as a dynamical map $\hatΛ(τ)$. Here we consider $\hatΛ(τ)$ arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales $\hatΛ(τ)$ is generically expected to be non-Markovian, however we do assume the ensuing dynamics has a unique steady state implying the baths possess a finite memory time $τ_{\rm m}$. By combining several techniques within a tensor network framework we directly and accurately extract $\hatΛ(τ)$ for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. We employ the Choi-Jamiolkowski isomorphism so that $\hatΛ(τ)$ can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxillary modes up to time $τ$. From $\hatΛ(τ)$ we also compute the time local propagator $\hat{\mathcal{L}}(τ)$. By examining the convergence with $τ$ of the instantaneous fixed points of these objects we establish their respective memory times $τ^Λ_{\rm m}$ and $τ^{\mathcal{L}}_{\rm m}$. Beyond these times, the propagator $\hat{\mathcal{L}}(τ)$ and dynamical map $\hatΛ(τ)$ accurately describe all the subsequent long-time relaxation dynamics up to stationarity. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit.

quant-ph↗

arXiv2024

Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach

Understanding the thermodynamics of driven quantum systems strongly coupled to thermal baths is a central focus of quantum thermodynamics and mesoscopic physics. A variety of different methodological approaches exist in the literature, all with their own advantages and disadvantages. The mesoscopic leads approach was recently generalised to steady state thermal machines and has the ability to replicate Landauer Büttiker theory in the non-interacting limit. In this approach a set of discretised lead modes, each locally damped, provide a markovian embedding for the baths. In this work we further generalise this approach to incorporate an arbitrary time dependence in the system Hamiltonian. Following a careful discussion of the calculation of thermodynamic quantities we illustrate the power of our approach by studying several driven mesoscopic examples coupled to finite temperature fermionic baths, replicating known results in various limits. In the case of a driven non interacting quantum dot we show how fast driving can be used to induce heat rectification.

quant-ph↗

arXiv2024

Arbitrary order transfer matrix exceptional points and van Hove singularities

In lattice models with quadratic finite-range Hermitian Hamiltonians, the inherently non-Hermitian transfer matrix (TM) governs the band dispersion. The van Hove singularities (VHSs) are special points in the band dispersion where the density of states (DOS) diverge. Considering a lattice chain with hopping of a finite range $n$, we find a direct fundamental connection between VHSs and exceptional points (EPs) of TM, both of arbitrary order. In particular, we show that VHSs are EPs of TM of the same order, thereby connecting two different types of critical points usually studied in widely different branches of physics. Consequently, several properties of band dispersion and VHSs can be analyzed in terms of spectral properties of TM. We further provide a general prescription to generate any order EP of the TM and therefore corresponding VHS. For a given range of hopping $n$, our analysis provides restrictions on allowed orders of EPs of TM. Finally, we exemplify all our results for the case $n=3$.

quant-ph↗

arXiv2024

Effect of order of transfer matrix exceptional points on transport at band edges

Recently, it has been shown that, in one dimensional fermionic systems, close to band edges, the zero temperature conductance scales as $1/N^2$, where $N$ is the system length. This universal subdiffusive scaling of conductance at band edges has been tied to an exceptional point (EP) of the transfer matrix of the system that occur at every band edge. Further, in presence of bulk dephasing probes, this EP has been shown to lead to a counterintuitive superballistic scaling of conductance, where the conductance increases with $N$ over a finite but large regime of system lengths. In this work, we explore how these behaviors are affected by the order of the transfer matrix EP at the band edge. We consider a one-dimensional fermionic lattice chain with a finite range of hopping. Depending on the range of hopping and the hopping parameters, this system can feature band edges which correspond to arbitrarily higher order EPs of the associated transfer matrix. Using this system we establish in generality that, in absence of bulk dephasing, surprisingly, the universal $1/N^2$ scaling of conductance is completely unaffected by the order of the EP. This is despite the fact that existence of transfer matrix EP is crucial for such behavior. In presence of bulk dephasing, however, the phase coherence length, the extent of the superballisitic scaling regime and the exponent of superballistic scaling, all encode the order of the transfer matrix EP.

cond-mat.mes-hall↗

arXiv2024

Non-Markovian Quantum Mpemba effect

Since it's rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received significant attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this work, we consider a general non-Markovian open quantum setting and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Due to non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, therefore giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and non-equilibrium setups at weak, intermediate and strong coupling, and both with and without interactions. Our work provides new insights into the rich physics underlying accelerated relaxation in quantum systems.

quant-ph↗

arXiv2024

Interaction-induced transition in quantum many-body detection probability

With the advent of digital and analog quantum simulation experiments, it is now possible to experimentally simulate dynamics of quantum many-body lattice systems and make site-resolved measurements. These experiments make it pertinent to consider the probability of getting any specific measurement outcome, which we call the `signal', on placing multiple detectors at various sites while simulating dynamics of a quantum many-body lattice system. In this work, we formulate and investigate this problem, introducing the concept of quantum many-body detection probability (QMBDP), which refers to the probability of detecting a chosen signal at least once in a given time. We show that, on tuning some Hamiltonian parameters, there can be sharp transition from a regime where QMBDP $\approx 1$, to a regime, where QMBDP $\approx 0$. Most notably, the effects of such a transition can be observed at a single trajectory level. This is not a measurement-induced transition, but rather a non-equilibrium transition reflecting opening of a specific type of gap in the many-body spectrum. We demonstrate this in a single-impurity non-integrable model, where changing the many-body interaction strength brings about such a transition. Our findings suggest that instead of measuring expectation values, single-shot stroboscopic measurements could be used to observe non-equilibrium transitions.

quant-ph↗

arXiv2024

Searching for Lindbladians obeying local conservation laws and showing thermalization

We investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. In order to preserve complete positivity and trace, such a QME must be of Lindblad form. For physical consistency, it should additionally preserve local conservation laws and be able to show thermalization. We search of Lindblad equations satisfying these additional criteria. First, we show that the microscopically derived Bloch-Redfield equation (RE) violates complete positivity unless in extremely special cases. We then prove that imposing complete positivity and demanding preservation of local conservation laws enforces the Lindblad operators and the lamb-shift Hamiltonian to be `local', i.e, to be supported only on the part of the system directly coupled to the bath. We then cast the problem of finding `local' Lindblad QME which can show thermalization into a semidefinite program (SDP). We call this the thermalization optimization problem (TOP). For given system parameters and temperature, the solution of the TOP conclusively shows whether the desired type of QME is possible up to a given precision. Whenever possible, it also outputs a form for such a QME. For a XXZ chain of few qubits, fixing a reasonably high precision, we find that such a QME is impossible over a considerably wide parameter regime when only the first qubit is coupled to the bath. Remarkably, we find that when the first two qubits are attached to the bath, such a QME becomes possible over much of the same paramater regime, including a wide range of temperatures.

quant-ph↗

arXiv2023

Environment assisted superballistic scaling of conductance

We find that, in the presence of weak incoherent effects from surrounding environments, the zero temperature conductance of nearest neighbour tight-binding chains exhibits a counter-intuitive power-law growth with system length at band-edges, indicating superballistic scaling. This fascinating environment assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This scaling regime can be systematically expanded by decreasing the coupling to the surrounding environments. There is no corresponding analog of this behavior for isolated systems. This superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band-edge.

cond-mat.mes-hall↗

arXiv2023

Nonclassical radiation from a nonlinear oscillator driven solely by classical $1/f$ noise

Low-frequency classical $1/f$-noise and quantum noise from low-temperature phonon modes are ubiquitous across various experimental platforms, and are usually considered a hindrance for quantum technological applications. Here we show that the simultaneous action of classical $1/f$ noise and a low-temperature phonon bath on a nonlinear oscillator can result in the generation of nonclassical antibunched radiation without the need for any additional drive. The $1/f$ noise itself provides the source of energy for generation of photons, while the phonon bath prevents heating up to infinite temperature and takes the nonlinear oscillator to a noise-averaged non-equilibrium steady state. The photon current in this non-equilibrium steady state may be detected by a standard wide-band detector. For sufficient nonlinearity and frequency dependence of the effective noise spectrum, the detected radiation can be antibunched. This opens the possibility to turn two of the most ubiquitous intrinsic noises in experimental platforms from a hindrance to a resource. It shows that wasteful heat from unavoidable noises can be converted into useful radiation. These results are based on the Redfield equation, which provides a rigorously derived general approach to treat any type of weak noise in a quantum system, specified only via the noise spectral function, as we discuss in detail.

quant-ph↗

arXiv2023

Particle current statistics in driven mesoscale conductors

We propose a highly-scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of non-zero temperature, strong coupling to terminals and in the presence of non-periodic light-matter interactions, away from equilibrium. The approach combines the so-called mesoscopic leads formalism with full counting statistics. It results in a generalised quantum master equation that dictates the dynamics of current fluctuations and higher order moments of the probability distribution function of charge exchange. For generic time-dependent quadratic Hamiltonians, we provide closed-form expressions for computing noise in the non-perturbative regime of the parameters of the system, reservoir or system-reservoir interactions. Having access to the full dynamics of the current and its noise, the method allows us to compute the variance of charge transfer over time in non-equilibrium configurations. The dynamics reveal that in driven systems, the average noise should be defined operationally with care over which period of time is covered.

quant-ph↗

arXiv2023

Universal subdiffusive behavior at band edges from transfer matrix exceptional points

We discover a deep connection between parity-time (PT) symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of $2 \times 2$ transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the PT-symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent $2$, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

quant-ph↗

arXiv2023

Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs

The simulation of open many-body quantum systems is challenging, requiring methods to both handle exponentially large Hilbert spaces and represent the influence of (infinite) particle and energy reservoirs. These two requirements are at odds with each other: Larger collections of modes can increase the fidelity of the reservoir representation but come at a substantial computational cost when included in numerical many-body techniques. An increasingly utilized and natural approach to control the growth of the reservoir is to cast a finite set of reservoir modes themselves as an open quantum system. There are, though, many routes to do so. Here, we introduce an accumulative reservoir construction -- an ARC -- that employs a series of partial refreshes of the extended reservoirs. Through this series, the representation accumulates the character of an infinite reservoir. This provides a unified framework for both continuous (Lindblad) relaxation and a recently introduced periodically refresh approach (i.e., discrete resets of the reservoir modes to equilibrium). In the context of quantum transport, we show that the phase space for physical behavior separates into discrete and continuous relaxation regimes with the boundary between them set by natural, physical timescales. Both of these regimes "turnover" into regions of over- and under-damped coherence in a way reminiscent of Kramers' crossover. We examine how the range of behavior impacts errors and the computational cost, including within tensor networks. These results provide the first comparison of distinct extended reservoir approaches, showing that they have different scaling of error versus cost (with a bridging ARC regime decaying fastest). Exploiting the enhanced scaling, though, will be challenging, as it comes with a substantial increase in (operator space) entanglement entropy.

quant-ph↗

arXiv2022

Quantum correlations in dissipative gain-loss systems across exceptional points

We investigate the behavior of correlations dynamics in a dissipative gain-loss system. First, we consider a setup made of two coupled lossy oscillators, with one of them subject to a local gain. This provides a more realistic platform to implement parity-time (PT) symmetry circumventing the implementation of a pure gain. We show how the qualitative dynamics of correlations resembles that for a pure-gain-loss setup. The major quantitative effect is that quantum correlations are reduced, while total ones are enhanced. Second, we study the behavior of these correlations across an exceptional point (EP) outside of the PT-symmetric regime of parameters, observing how different behaviors across the EP occur only in the transient dynamics. This shows how PT symmetry plays a relevant role at large times.

quant-ph↗