arXiv subjects

Manas Kulkarni

Publications and source records attributed to Manas Kulkarni.

At least 73 records · Page 4Linked to original sources

arXiv2023

Nonequilibrium spin transport in integrable and non-integrable classical spin chains

Anomalous transport in low dimensional spin chains is an intriguing topic that can offer key insights into the interplay of integrability and symmetry in many-body dynamics. Recent studies have shown that spin-spin correlations in spin chains, where integrability is either perfectly preserved or broken by symmetry-preserving interactions, fall in the Kardar-Parisi-Zhang (KPZ) universality class. Similarly, energy transport can show ballistic or diffusive-like behaviour. Although such behaviour has been studied under equilibrium conditions, no results on nonequilibrium spin transport in classical spin chains has been reported so far. In this work, we investigate both spin and energy transport in classical spin chains (integrable and non-integrable) when coupled to two reservoirs at two different temperatures/magnetization. In both the integrable case and broken-integrability (but spin-symmetry preserving), we report anomalous scaling of spin current with system size ($\mathbb{J}^s \propto L^{-μ}$) with an exponent, $μ\approx 2/3$, falling under the KPZ universality class. On the other hand, it is noteworthy that energy current remains ballistic ($\mathbb{J}^e \propto L^{-η}$ with $η\approx 0$) in the purely integrable case and there is departure from ballistic behaviour ($η> 0$) when integrability is broken regardless of spin-symmetry. Under nonequilibrium conditions, we have thoroughly investigated spatial profiles of local magnetization and energy. We find interesting nonlinear spatial profiles which are hallmarks of anomalous transport. We also unravel subtle striking differences between the equilibrium and nonequilibrium steady state through the lens of spatial spin-spin correlations.

cond-mat.stat-mech↗

arXiv2023

First detection probability in quantum resetting via random projective measurements

We provide a general framework to compute the probability distribution $F_r(t)$ of the first detection time of a 'state of interest' in a generic quantum system subjected to random projective measurements. In our 'quantum resetting' protocol, resetting of a state is not implemented by an additional classical stochastic move, but rather by the random projective measurement. We then apply this general framework to Poissoinian measurement protocol with a constant rate $r$ and demonstrate that exact results for $F_r(t)$ can be obtained for a generic two level system. Interestingly, the result depends crucially on the detection schemes involved and we have studied two complementary schemes, where the state of interest either coincides or differs from the initial state. We show that $F_r(t)$ at short times vanishes universally as $F_r(t)\sim t^2$ as $t\to 0$ in the first scheme, while it approaches a constant as $t\to 0$ in the second scheme. The mean first detection time, as a function of the measurement rate $r$, also shows rather different behaviors in the two schemes. In the former, the mean detection time is a nonmonotonic function of $r$ with a single minimum at an optimal value $r^*$, while in the later, it is a monotonically decreasing function of $r$, signalling the absence of a finite optimal value. These general predictions for arbitrary two level systems are then verified via explicit computation in the Jaynes-Cummings model of light-matter interaction. We also generalise our results to non-Poissonian measurement protocols with a renewal structure where the intervals between successive independent measurements are distributed via a general distribution $p(τ)$ and show that the short time behavior of $F_r(t)\sim p(0)\, t^2$ is universal as long as $p(0)\ne 0$. This universal $t^2$ law emerges from purely quantum dynamics that dominates at early times.

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

Boltzmann entropy of a freely expanding quantum ideal gas

We study the time evolution of the Boltzmann entropy of a microstate during the non-equilibrium free expansion of a one-dimensional quantum ideal gas. This quantum Boltzmann entropy, $S_B$, essentially counts the "number" of independent wavefunctions (microstates) giving rise to a specified macrostate. It generally depends on the choice of macrovariables, such as the type and amount of coarse-graining, specifying a non-equilibrium macrostate of the system, but its extensive part agrees with the thermodynamic entropy in thermal equilibrium macrostates. We examine two choices of macrovariables: the $U$-macrovariables are local observables in position space, while the $f$-macrovariables also include structure in momentum space. For the quantum gas, we use a non-classical choice of the $f$-macrovariables. For both choices, the corresponding entropies $s_B^f$ and $s_B^U$ grow and eventually saturate. As in the classical case, the growth rate of $s_B^f$ depends on the momentum coarse-graining scale. If the gas is initially at equilibrium and is then released to expand to occupy twice the initial volume, the per-particle increase in the entropy for the $f$-macrostate, $Δs_B^f$, satisfies $\log{2}\leqΔs_B^f\leq 2\log{2}$ for fermions, and $0\leqΔs_B^f\leq\log{2}$ for bosons. For the same initial conditions, the change in the entropy $Δs_B^U$ for the $U$-macrostate is greater than $Δs_B^f$ when the gas is in the quantum regime where the final stationary state is not at thermal equilibrium.

cond-mat.stat-mech↗

arXiv2022

Finite temperature equilibrium density profiles of integrable systems in confining potentials

We study the equilibrium density profile of particles in two one-dimensional classical integrable models, namely hard rods and the hyperbolic Calogero model, placed in confining potentials. For both of these models the inter-particle repulsion is strong enough to prevent particle trajectories from intersecting. We use field theoretic techniques to compute the density profile and their scaling with system size and temperature, and compare them with results from Monte-Carlo simulations. In both cases we find good agreement between the field theory and simulations. We also consider the case of the Toda model in which inter-particle repulsion is weak and particle trajectories can cross. In this case, we find that a field theoretic description is ill-suited due to the lack of a thermodynamic length scale. The density profiles for the Toda model obtained from Monte-Carlo simulations can be understood by studying the analytically tractable harmonic chain model (Hessian approximation of the Toda model). For the harmonic chain model one can derive an exact expression for the density that shines light on some of the qualitative features of the Toda model in a quadratic trap. Our work provides an analytical approach towards understanding the equilibrium properties for interacting integrable systems in confining traps.

cond-mat.stat-mech↗

arXiv2022

Filling an empty lattice by local injection of quantum particles

We study the quantum dynamics of filling an empty lattice of size $L$, by connecting it locally with an equilibrium thermal bath that injects non-interacting bosons or fermions. We adopt four different approaches, namely (i) direct exact numerics, (ii) Redfield equation, (iii) Lindblad equation, and (iv) quantum Langevin equation -- which are unique in their ways for solving the time dynamics and the steady-state. Our setup offers a simplistic platform to understand fundamental aspects of dynamics and approach to thermalization. The quantities of interest that we consider are the spatial density profile and the total number of bosons/fermions in the lattice. The spatial spread is ballistic in nature and the local occupation eventually settles down owing to equilibration. The ballistic spread of local density admits a universal scaling form. We show that this universality is only seen when the condition of detailed balance is satisfied by the baths. The difference between bosons and fermions shows up in the early time growth rate and the saturation values of the profile. The techniques developed here are applicable to systems in arbitrary dimensions and for arbitrary geometries.

quant-ph↗

arXiv2022

Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature

We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $Ω$ and in the presence of an additional repulsive central potential $γ/r^2$. The average density at zero temperature was recently studied in Phys. Rev. A $\textbf{103}$, 033321 (2021) and an interesting multi-layered "wedding cake" structure with a "hole" at the center was found for the density in the large $N$ limit. In this paper, we study the average density at finite temperature. We demonstrate how this "wedding-cake" structure is modified at finite temperature. These large $N$ results warrant going much beyond the standard Local Density Approximation. We also generalize our results to a wide variety of trapping potentials and demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the "wedding-cake".

cond-mat.stat-mech↗

arXiv2022

Spectral Properties of Disordered Interacting Non-Hermitian Systems

Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian interacting disordered Hamiltonians and attempt to analyze their chaotic behavior or lack of it through the lens of the recently introduced non-hermitian analog of the spectral form factor and the complex spacing ratio. We consider three widely relevant non-hermitian models which are unique in their ways and serve as excellent platforms for such investigations. Two of the models considered are short-ranged and have different symmetries. The third model is long-ranged, whose hermitian counterpart has itself become a subject of growing interest. All these models exhibit a deep connection with the non-hermitian Random Matrix Theory of corresponding symmetry classes at relatively weak disorder. At relatively strong disorder, the models show the absence of complex eigenvalue correlation, thereby, corresponding to Poisson statistics. Our thorough analysis is expected to play a crucial role in understanding disordered open quantum systems in general.

cond-mat.dis-nn↗

arXiv2022

Gap Statistics for Confined Particles with Power-Law Interactions

We consider the $N$ particle classical Riesz gas confined in a one-dimensional external harmonic potential with power law interaction of the form $1/r^k$ where $r$ is the separation between particles. As special limits it contains several systems such as Dyson's log-gas ($k\to 0^+$), Calogero-Moser model ($k=2$), 1d one component plasma ($k=-1$) and the hard-rod gas ($k\to \infty$). Despite its growing importance, only large-$N$ field theory and average density profile are known for general $k$. In this Letter, we study the fluctuations in the system by looking at the statistics of the gap between successive particles. This quantity is analogous to the well-known level spacing statistics which is ubiquitous in several branches of physics. We show that the variance goes as $N^{-b_k}$ and we find the $k$ dependence of $b_k$ via direct Monte Carlo simulations. We provide supporting arguments based on microscopic Hessian calculation and a quadratic field theory approach. We compute the gap distribution and study its system size scaling. Except in the range $-1 -2$ with both Gaussian and non-Gaussian scaling forms.

cond-mat.stat-mech↗

arXiv2022

Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability

Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and Kardar-Parisi-Zhang (KPZ) universality class has emerged. Theoretical developments (e.g. generalized hydrodynamics) have highlighted the role of integrability as well as spin-symmetry in KPZ behaviour. However understanding their precise role on superdiffusive transport still remains a challenging task. The widely used quantum spin chain platform comes with severe numerical limitations. To circumvent this barrier, we focus on a classical integrable spin chain which was shown to have deep analogy with the quantum spin-$\frac{1}{2}$ Heisenberg chain. Remarkably, we find that KPZ behaviour prevails even when one considers integrability-breaking but spin-symmetry preserving terms, strongly indicating that spin-symmetry plays a central role even in the non-perturbative regime. On the other hand, in the non-perturbative regime, we find that energy correlations exhibit clear diffusive behaviour. We also study the classical analog of out-of-time-ordered correlator (OTOC) and Lyapunov exponents. We find significant presence of chaos for the integrability-broken cases even though KPZ behaviour remains robust. The robustness of KPZ behaviour is demonstrated for a wide class of spin-symmetry preserving integrability-breaking terms.

cond-mat.stat-mech↗

arXiv2022

Localization and delocalization in networks with varied connectivity

We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we consider (i) Harmonic (ii) Jaynes-Cummings and (iii) Bose-Hubbard networks. We start with the initial condition where one of the nodes in the network is populated and then let it evolve in time. The time dynamics and steady state characterize the features of localization (self-trapping) in these large-scale networks. For the case of Harmonic networks, exact analytical results are obtained and we demonstrate that all-to-all connection shows self-trapping whereas the finite-ranged connectivity shows delocalization. The interacting cases (Jaynes-Cummings, Bose-Hubbard networks) are investigated both via exact quantum dynamics and semi-classical approach. We obtain an interesting phase diagram when one varies the range of connectivity and the strength of the interaction. We investigate the consequence of imperfections in the cavity/qubit and the role of inevitable disorder. Our results are relevant especially given recent experimental progress in engineering systems with long-range connectivity.

quant-ph↗

arXiv2022

Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths

It is very common in the literature to write down a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in system-bath coupling is of the so-called Redfield form which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundamental requirements for any further approximations to Redfield equation, which, if violated, leads to physical inconsistencies like inaccuracies in the leading order populations and coherences in the energy eigenbasis, violation of thermalization, violation of local conservation laws at the non-equilibrium steady state (NESS). We argue that one or more of these conditions will generically be violated in all the weak system-bath-coupling Lindblad descriptions existing in literature to our knowledge. As an example, we study the recently derived Universal Lindblad Equation (ULE) and use these conditions to show violation of local conservation laws due to inaccurate coherences but accurate populations in energy eigenbasis. Finally, we exemplify our analytical results numerically in an interacting open quantum spin system.

quant-ph↗

arXiv2021

Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap

We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $Ω$ in the presence of an additional repulsive central potential $γ/r^2$. We find that, in the large $N$ limit, the bulk density has a rich and nontrivial profile -- with a hole at the center of the trap and surrounded by a multi-layered "wedding cake" structure. The number of layers depends on $N$ and on the two parameters $Ω$ and $γ$ leading to a rich phase diagram. Zooming in on the edge of the $k^{\rm th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\rm th}$ Hermite polynomial. Interestingly, in the large $k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.

cond-mat.stat-mech↗

arXiv2021

Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices

We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in open quantum systems. We establish that the Liouvillian describing the quantum dynamics exhibits distinct spectral features of integrable and chaotic character on the two sides of the critical point. We follow the distribution of the spacings of the complex Liouvillian eigenvalues across the critical point. In the normal and superradiant phases, the distributions are $2D$ Poisson and that of the Ginibre Unitary random matrix ensemble, respectively. Our results are corroborated by computing a recently introduced complex-plane generalization of the consecutive level-spacing ratio distribution. Our approach can be readily adapted for classifying the nature of quantum dynamics across dissipative critical points in other open quantum systems.

quant-ph↗

arXiv2021

Edge fluctuations and third-order phase transition in harmonically confined long-range systems

We study the distribution of the position of the rightmost particle $x_{\max}$ in a $N$-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive potential, of the form $r^{-k}$ with $-2 -2$. We also find that these large deviation functions describe a pulled to pushed type phase transition as observed in Dyson's log-gas ($k\to 0$) and $1d$ one component plasma ($k=-1$). Remarkably, we find that the phase transition remains $3^{\rm rd}$ order for the entire regime. Our results demonstrate the striking universality of the $3^{\rm rd}$ order transition even in models that fall outside the paradigm of Coulomb systems and the random matrix theory. We numerically verify our analytical expressions of the large deviation functions via Monte Carlo simulation using an importance sampling algorithm.

cond-mat.stat-mech↗

arXiv2021

Quasiparticle kinetic theory for Calogero models

We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe-Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.

cond-mat.stat-mech↗

arXiv2021

Harmonically confined long-ranged interacting gas in the presence of a hard wall

In this paper, we compute exactly the average density of a harmonically confined Riesz gas of $N$ particles for large $N$ in the presence of a hard wall. In this Riesz gas, the particles repel each other via a pairwise interaction that behaves as $|x_i - x_j|^{-k}$ for $k>-2$, with $x_i$ denoting the position of the $i^{\rm th}$ particle. This density can be classified into three different regimes of $k$. For $k \geq 1$, where the interactions are effectively short-ranged, the appropriately scaled density has a finite support over $[-l_k(w),w]$ where $w$ is the scaled position of the wall. While the density vanishes at the left edge of the support, it approaches a nonzero constant at the right edge $w$. For $-1<k<1$, where the interactions are weakly long-ranged, we find that the scaled density is again supported over $[-l_k(w),w]$. While it still vanishes at the left edge of the support, it diverges at the right edge $w$ algebraically with an exponent $(k-1)/2$. For $-2<k< -1$, the interactions are strongly long-ranged that leads to a rather exotic density profile with an extended bulk part and a delta-peak at the wall, separated by a hole in between. Exactly at $k=-1$ the hole disappears. For $-2<k< -1$, we find an interesting first-order phase transition when the scaled position of the wall decreases through a critical value $w=w^*(k)$. For $w<w^*(k)$, the density is a pure delta-peak located at the wall. The amplitude of the delta-peak plays the role of an order parameter which jumps to the value $1$ as $w$ is decreased through $w^*(k)$. Our analytical results are in very good agreement with our Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2021

Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain

We show that the one dimensional discrete nonlinear Schrödinger chain (DNLS) at finite temperature has three different dynamical regimes (ultra-low, low and high temperature regimes). This has been established via (i) one point macroscopic thermodynamic observables (temperature $T$ , energy density $ε$ and the relationship between them), (ii) emergence and disappearance of an additional almost conserved quantity (total phase difference) and (iii) classical out-of-time-ordered correlators (OTOC) and related quantities (butterfly speed and Lyapunov exponents). The crossover temperatures $T_{\textit{l-ul}}$ (between low and ultra-low temperature regimes) and $T_{\textit{h-l}}$ (between high and low temperature regimes) extracted from these three different approaches are consistent with each other. The analysis presented here is an important step forward towards the understanding of DNLS which is ubiquitous in many fields and has a non-separable Hamiltonian form. Our work also shows that the different methods used here can serve as important tools to identify dynamical regimes in other interacting many body systems.

cond-mat.stat-mech↗