arXiv subjects

Vijay Ganesh Sadhasivam

Publications and source records attributed to Vijay Ganesh Sadhasivam.

8 recordsLinked to original sources

arXiv2026

Effective classical potential for quantum statistical averages

We present an effective potential that allows quantum thermal expectation values of a position-dependent observable to be estimated as a classical ensemble average of the corresponding function. We follow the approach of Feynman and Hibbs, but perform the mean-field treatment of quantum fluctuations about the path starting point rather than the path centroid. Furthermore, rather than performing a full variational optimization of the potential, we explore approximate functional forms that yield a numerical robustness. The resulting closed-form potential is exact in the classical and harmonic limits; benchmarks against exact position distributions for one-dimensional quartic, Morse, and double-well potentials, show good agreement for potentials with harmonic support.

quant-ph↗

arXiv2025

On the origin of exponential operator growth in Hilbert space

The question of thermalization in quantum many-body systems has long been studied through the properties of matrix elements of operators corresponding to local observables. More recently, the focus has shifted to the dynamics of operators, which lead to seminal works proposing universal bounds on the rate of operator growth. In this work, we unify these two approaches: we show that exponential operator growth in Hilbert space, as measured by Krylov complexity, is governed by an exponential off-diagonal decay of the operator matrix elements in the system eigenbasis. When this decay is algebraic or slower, the growth rate saturates the universal bound, thereby establishing a microscopic origin of operator growth which is independent of chaos, dimensionality or the presence of many-body interactions.

quant-ph↗

arXiv2024

Parametric tuning of quantum phase transitions in ultracold reactions

Advances in atomic physics have led to the possibility of a coherent transformation between ultra-cold atoms and molecules including between completely bosonic condensates. Such transformations are enabled by the magneto-association of atoms at a Feshbach resonance which results in a passage through a quantum critical point. In this study, we show that the presence of generic interaction between the constituent atoms and molecules can fundamentally alter the nature of the critical point, change the yield of the reaction and the order of the consequent phase transition. We find that the correlations introduced by this interaction induce nontrivial many-body physics such as coherent oscillations between atoms and molecules, and a selective formation of squeezed molecular quantum states and quantum cat states. We provide analytical and numerical descriptions of these effects, along with scaling laws for the reaction yield in non-adiabatic regimes.

cond-mat.quant-gas↗

arXiv2024

Thermal quenching of classical and semiclassical scrambling

Quantum scrambling often gives rise to short-time exponential growth in out-of-time-ordered correlators (OTOCs). The scrambling rate over an isolated saddle point at finite temperature is shown here to be reduced by a hierarchy of quenching processes. Two of these appear in the classical limit, where escape from the neighbourhood of the saddle reduces the rate by a factor of two, and thermal fluctuations around the saddle reduce it further; a third process can be explained semiclassically as arising from quantum thermal fluctuations around the saddle, which are also responsible for imposing the Maldacena-Shenker-Stanford bound.

nlin.CD↗

arXiv2024

Nonadiabatic transitions during a passage near a critical point

The passage through a critical point of a many-body quantum system leads to abundant nonadiabatic excitations. Here, we explore a regime, in which the critical point is not crossed although the system is passing slowly very close to it. We show that the leading exponent for the excitation probability then can be obtained by standard arguments of the Dykhne formula but the exponential prefactor is no longer simple, and behaves as a power law on the characteristic transition rate. We derive this prefactor for the nonlinear Landau-Zener (nLZ) model by adjusting the Dykhne's approach. Then, we introduce an exactly solvable model of the transition near a critical point in the Stark ladder. We derive the number of the excitations for it without approximations, and find qualitatively similar results for the excitation scaling.

cond-mat.stat-mech↗

arXiv2023

Instantons and the quantum bound to chaos

We investigate why the Lyapunov exponents $λ$ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound $λ< 2 πk_B T/{\hbar}$ by probing imaginary-time path-integral space using ring-polymer molecular dynamics (RPMD) for a barrier-crossing model. We find that the RPMD OTOC satisfies the same bound as the quantum OTOC, which is caused by the stability of quantum thermal fluctuations around the instanton on the barrier. We expect that similar instantons (or other delocalised structures) will be found in many other systems with exponentially growing OTOCs.

quant-ph↗

arXiv2022

Stochastic model for barrier crossings and fluctuations in local timescale

The problem of computing the rate of diffusion-aided activated barrier crossings between metastable states is one of broad relevance in physical sciences. The transition path formalism aims to compute the rate of these events by analysing the statistical properties of the transition path between the two metastable regions concerned. In this paper, we show that the transition path process is a unique solution to an associated stochastic differential equation (SDE), with a discontinuous and singular drift term. The singularity arises from a local time contribution, which accounts for the fluctuations at the boundaries of the metastable regions. The presence of fluctuations at the local time scale calls for an excursion theoretic consideration of barrier crossing events. We show that the rate of such events, as computed from excursion theory, factorizes into a local time term and an excursion measure term, which bears empirical similarity to the transition state theory rate expression. Since excursion theory makes no assumption about the presence of a transition state in the potential energy landscape, the mathematical structure underlying this factorization ought to be general. We hence expect excursion theory (and local times) to provide some physical and mathematical insights in generic barrier crossing problems.

cond-mat.stat-mech↗

arXiv2021

Testing the quasicentroid molecular dynamics method on gas-phase ammonia

Quasicentroid molecular dynamics (QCMD) is a path-integral method for approximating nuclear quantum effects in dynamics simulations, which has given promising results for gas- and condensed-phase water. Here, by simulating the infrared spectrum of gas-phase ammonia, we test the feasibility of extending QCMD beyond water. Overall, QCMD works as well for ammonia as for water, reducing or eliminating blue shifts from the classical spectrum without introducing the artificial red-shifts or broadening associated with other imaginary-time path-integral methods. However, QCMD gives only a modest improvement over the classical spectrum for the position of the symmetric bend mode, which is highly anharmonic (since it correlates with the inversion pathway). We expect QCMD to have similar problems with large-amplitude degrees of freedom in other molecules, but otherwise to work as well as for water.

physics.chem-ph↗