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Manas Kulkarni

Publications and source records attributed to Manas Kulkarni.

At least 55 records · Page 3Linked to original sources
arXiv2024

Anomalous transport in long-ranged open quantum systems

We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $α$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a non-equilibrium steady state charge transport, and (ii) time dynamics of an initially localized single particle excitation in the absence of boundary reservoirs. In both variants, anomalous super-diffusive behavior is observed for $1< α< 1.5$, and for $α> 1.5$ the setup is effectively short-ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple-scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behaviour in open quantum systems.

cond-mat.stat-mech↗
arXiv2024

Quantum jumps in driven-dissipative disordered many-body systems

We discuss how quantum jumps affect localized regimes in driven-dissipative disordered many-body systems featuring a localization transition. We introduce a deformation of the Lindblad master equation that interpolates between the standard Lindblad and the no-jump non-Hermitian dynamics of open quantum systems. As a platform, we use a disordered chain of hard-core bosons with nearest-neighbor interactions and subject to incoherent drive and dissipation at alternate sites. We probe both the statistics of complex eigenvalues of the deformed Liouvillian and dynamical observables of physical relevance. We show that reducing the number of quantum jumps, achievable through realistic postselection protocols, can promote the emergence of the localized phase. Our findings are based on exact diagonalization and time-dependent matrix-product states techniques.

quant-ph↗
arXiv2024

Ergodic and chaotic properties in Tavis-Cummings dimer: quantum and classical limit

We investigate two key aspects of quantum systems by using the Tavis-Cummings dimer system as a platform. The first aspect involves unraveling the relationship between the phenomenon of self-trapping (or lack thereof) and integrability (or quantum chaos). Secondly, we uncover {the possibility of} mixed behavior in this quantum system using diagnostics based on random matrix theory and make an in-depth study of classical-quantum correspondence. The setup chosen for the study is precisely suited as it (i) enables a transition from delocalized to self-trapped states and (ii) has a well-defined classical limit, thereby amenable to studies involving classical-quantum conjectures. The obtained classical model in itself has rich chaotic and ergodic properties which were probed via maximal Lyapunov exponents. Furthermore, we present aspects of chaos in the corresponding open quantum system and make connections with non-Hermitian random matrix theory.

quant-ph↗
arXiv2024

Full counting statistics of 1d short-range Riesz gases in confinement

We investigate the full counting statistics (FCS) of a harmonically confined 1d short-range Riesz gas consisting of $N$ particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent $k>1$ which includes the Calogero-Moser model for $k=2$. We examine the probability distribution of the number of particles in a finite domain $[-W, W]$ called number distribution, denoted by $\mathcal{N}(W, N)$. We analyze the probability distribution of $\mathcal{N}(W, N)$ and show that it exhibits a large deviation form for large $N$ characterised by a speed $N^{\frac{3k+2}{k+2}}$ and by a large deviation function of the fraction $c = \mathcal{N}(W, N)/N$ of the particles inside the domain and $W$. We show that the density profiles that create the large deviations display interesting shape transitions as one varies $c$ and $W$. This is manifested by a third-order phase transition exhibited by the large deviation function that has discontinuous third derivatives. Monte-Carlo (MC) simulations show good agreement with our analytical expressions for the corresponding density profiles. We find that the typical fluctuations of $\mathcal{N}(W, N)$, obtained from our field theoretic calculations are Gaussian distributed with a variance that scales as $N^{ν_k}$, with $ν_k = (2-k)/(2+k)$. We also present some numerical findings on the mean and the variance. Furthermore, we adapt our formalism to study the index distribution (where the domain is semi-infinite $(-\infty, W])$, linear statistics (the variance), thermodynamic pressure and bulk modulus.

cond-mat.stat-mech↗
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↗
arXiv2024

Generalised Hydrodynamics description of the Page curve-like dynamics of a freely expanding fermionic gas

We consider an analytically tractable model that exhibits the main features of the Page curve characterizing the evolution of entanglement entropy during evaporation of a black hole. Our model is a gas of non-interacting fermions on a lattice that is released from a box into the vacuum. More precisely, our Hamiltonian is a tight-binding model with a defect at the junction between the filled box and the vacuum. In addition to the entanglement entropy we consider several other observables, such as the spatial density profile and current, and show that the semiclassical approach of generalized hydrodynamics provides a remarkably accurate description of the quantum dynamics including that of the entanglement entropy at all times. Our hydrodynamic results agree closely with those obtained via exact microscopic numerics. We find that the growth of entanglement is linear and universal, i.e, independent of the details of the defect. The decay shows $1/t$ scaling for conformal defect while for non-conformal defects, it is slower. Our study shows the power of the semiclassical approach and could be relevant for discussions on the resolution of the black hole information paradox.

quant-ph↗
arXiv2024

Universality in coupled stochastic Burgers systems with degenerate flux Jacobian

In our contribution we study stochastic models in one space dimension with two conservation laws. One model is the coupled continuum stochastic Burgers equation, for which each current is a sum of quadratic non-linearities, linear diffusion, and spacetime white noise. The second model is a two-lane stochastic lattice gas. As distinct from previous studies, the two conserved densities are tuned such that the flux Jacobian, a $2 \times 2$ matrix, has coinciding eigenvalues. In the steady state, investigated are spacetime correlations of the conserved fields and the time-integrated currents at the origin. For a particular choice of couplings the dynamical exponent 3/2 is confirmed. Furthermore, at these couplings, continuum stochastic Burgers equation and lattice gas are demonstrated to be in the same universality class.

cond-mat.stat-mech↗
arXiv2023

Long-ranged spectral correlations in eigenstate phases

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.

cond-mat.dis-nn↗
arXiv2023

Dynamically emergent correlations between particles in a switching harmonic trap

We study a one dimensional gas of $N$ noninteracting diffusing particles in a harmonic trap, whose stiffness switches between two values $μ_1$ and $μ_2$ with constant rates $r_1$ and $r_2$ respectively. Despite the absence of direct interaction between the particles, we show that strong correlations between them emerge in the stationary state at long times, induced purely by the dynamics itself. We compute exactly the joint distribution of the positions of the particles in the stationary state, which allows us to compute several physical observables analytically. In particular, we show that the extreme value statistics (EVS), i.e., the distribution of the position of the rightmost particle has a nontrivial shape in the large $N$ limit. The scaling function characterizing this EVS has a finite support with a tunable shape (by varying the parameters). Remarkably, this scaling function turns out to be universal. First, it also describes the distribution of the position of the $k$-th rightmost particle in a $1d$ trap. Moreover, the distribution of the position of the particle farthest from the center of the harmonic trap in $d$ dimensions is also described by the same scaling function for all $d \geq 1$. Numerical simulations are in excellent agreement with our analytical predictions.

cond-mat.stat-mech↗
arXiv2023

Transition to chaos in extended systems and their quantum impurity models

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model on a finite chain. By studying level-spacing statistics, adjacent gap ratios, and spectral form factors, we observe the transition from integrability to chaos as the hopping between the Tavis-Cummings sites is increased above a finite value. The results are obtained by means of exact numerical diagonalization which becomes notoriously hard for extended lattice geometries. In an attempt to circumvent these difficulties, we identify a minimal single-site quantum impurity model that successfully captures the spectral properties of the lattice model. This approach is intended to be adaptable to other lattice models with large local Hilbert spaces.

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

Exceptional hypersurfaces of transfer matrices of finite-range lattice models and their consequences on quantum transport properties

We investigate the emergence and corresponding nature of exceptional points located on exceptional hyper-surfaces of non-hermitian transfer matrices for finite-range one-dimensional lattice models. We unravel the non-trivial role of these exceptional points in determining the system size scaling of electrical conductance in non-equilibrium steady state. We observe that the band edges of the system always correspond to the transfer matrix exceptional points. Interestingly, albeit the lower band edge always occurs at wave-vector $k=0$, the upper band edge may or may not correspond to $k=π$. Nonetheless, in all the cases, the system exhibits universal subdiffusive transport for conductance at every band edge with scaling $N^{-b}$ with scaling exponent $b= 2$. However, for cases when the upper band edge is not located at $k=π$, the conductance features interesting oscillations with overall $N^{-2}$ scaling. Our work further reveals that this setup is uniquely suited to systematically generate higher order transfer matrix exceptional points at upper band edge when one considers finite range hoppings beyond nearest neighbour. Additional exceptional points other than those at band edges are shown to occur, although interestingly, these do not give rise to anomalous transport.

cond-mat.mes-hall↗
arXiv2023

Impact of dephasing probes on incommensurate lattices

We investigate open quantum dynamics for a one-dimensional incommensurate Aubry-André-Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behaviour in time that has no parallel in the isolated case (\emph{i.e.}, in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behaviour, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behaviour. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.

cond-mat.stat-mech↗
arXiv2023

Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices

The dynamics of non-Hermitian quantum systems have taken on an increasing relevance in light of quantum devices which are not perfectly isolated from their environment. The interest in them also stems from their fundamental differences from their Hermitian counterparts, particularly with regard to their spectral and eigenvector correlations. These correlations form the fundamental building block for understanding the dynamics of quantum systems as all other correlations can be reconstructed from it. In this work, we study such correlations across a localisation transition in non-Hermitian quantum systems. As a concrete setting, we consider non-Hermitian power-law banded random matrices which have emerged as a promising platform for studying localisation in disordered, non-Hermitian systems. We show that eigenvector correlations show marked differences between the delocalised and localised phases. In the delocalised phase, the eigenvectors are strongly correlated as evinced by divergent correlations in the limit of vanishingly small complex eigenvalue spacings. On the contrary, in the localised phase, the correlations are independent of the eigenvalue spacings. We explain our results in the delocalised phase by appealing to the Ginibre random matrix ensemble. On the other hand, in the localised phase, an analytical treatment sheds light on the suppressed correlations, relative to the delocalised phase. Given that eigenvector correlations are fundamental ingredients towards understanding real- and imaginary-time dynamics with non-Hermitian generators, our results open a new avenue for characterising dynamical phases in non-Hermitian quantum many-body systems.

cond-mat.dis-nn↗
arXiv2023

Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations

The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems. Here, we study the (classical) OTOC and its ``light-cone'' in the nonlinear Kuramoto-Sivashinsky (KS) equation, using extensive numerical simulations. We also show that the linearized KS equation exhibits a qualitatively similar OTOC and light-cone, which can be understood via a saddle-point analysis of the linearly unstable modes. Given the deep connection between the KS (deterministic) and the Kardar-Parisi-Zhang (KPZ which is stochastic) equations, we also explore the OTOC in the KPZ equation. While our numerical results in the KS case are expected to hold in the continuum limit, for the KPZ case it is valid in a discretized version of the KPZ equation. More broadly, our work unravels the intrinsic interplay between noise/instability, nonlinearity and dissipation in partial differential equations (deterministic or stochastic) through the lens of OTOC.

cond-mat.stat-mech↗
arXiv2023

Generating Entanglement by Quantum Resetting

We consider a closed quantum system subjected to stochastic Poissonian resetting with rate $r$ to its initial state. Resetting drives the system to a nonequilibrium stationary state (NESS) with a mixed density matrix which has both classical and quantum correlations. We provide a general framework to study these NESS correlations for a closed quantum system with a general Hamiltonian $H$. We then apply this framework to a simple model of a pair of ferromagnetically coupled spins, starting from state $\mid\downarrow\downarrow \rangle$ and resetting to the same state with rate $r$. We compute exactly the NESS density matrix of the full system. This then provides access to three basic observables, namely (i) the von Neumann entropy of a subsystem (ii) the fidelity between the NESS and the initial density matrix and (iii) the concurrence in the NESS (that provides a measure of the quantum entanglement in a mixed state), as a function of the two parameters: the resetting rate and the interaction strength. One of our main conclusions is that a nonzero resetting rate and a nonzero interaction strength generates quantum entanglement in the NESS (quantified by a nonzero concurrence) and moreover this concurrence can be maximized by appropriately choosing the two parameters. Our results show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of an interacting quantum system.

quant-ph↗
arXiv2023

Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases

Caustics are singularities that occur naturally in optical, hydrodynamic and quantum waves, giving rise to high amplitude patterns that can be described using catastrophe theory. In this paper we study caustics in a statistical field theory setting in the form of the sine-Gordon model that describes a variety of physical systems including coupled 1D superfluids. Specifically, we use classical field simulations to study the dynamics of two ultracold 1D Bose gases (quasi-condensates) that are suddenly coupled to each other and find that the resulting non-equilibrium dynamics are dominated by caustics. Thermal noise is included by sampling the initial states from a Boltzmann distribution for phononic excitations. We find that caustics pile up over time in both the number and phase difference observables leading to a characteristic non-thermal `circus tent' shaped probability distribution at long times.

cond-mat.quant-gas↗
arXiv2023

Unusual ergodic and chaotic properties of trapped hard rods

We investigate ergodicity, chaos and thermalization for a one-dimensional classical gas of hard rods confined to an external quadratic or quartic trap, which breaks microscopic integrability. To quantify the strength of chaos in this system, we compute its maximal Lyapunov exponent numerically. The approach to thermal equilibrium is studied by considering the time evolution of particle position and velocity distributions and comparing the late-time profiles with the Gibbs state. Remarkably, we find that quadratically trapped hard rods are highly non-ergodic and do not resemble a Gibbs state even at extremely long times, despite compelling evidence of chaos for four or more rods. On the other hand, our numerical results reveal that hard rods in a quartic trap exhibit both chaos and thermalization, and equilibrate to a Gibbs state as expected for a nonintegrable many-body system.

cond-mat.stat-mech↗