Uma Divakaran

Bio: Uma Divakaran is an academic researcher from Indian Institutes of Technology. The author has contributed to research in topics: Quantum phase transition & Quantum critical point. The author has an hindex of 15, co-authored 54 publications receiving 883 citations. Previous affiliations of Uma Divakaran include Saarland University & Indian Institute of Technology Kanpur.

Effect of double local quenches on the Loschmidt echo and entanglement entropy of a one-dimensional quantum system

Abstract: We study the effect of two simultaneous local quenches on the evolution of the Loschmidt echo (LE) and entanglement entropy (EE) of a one dimensional transverse Ising model. In this work, one of the local quenches involves the connection of two spin-1/2 chains at a certain time and the other corresponds to a sudden change in the magnitude of the transverse field at a given site in one of the spin chains. We numerically calculate the dynamics associated with the LE and the EE as a result of such double quenches, and discuss the various timescales involved in this problem using the picture of quasiparticles (QPs) generated as a result of such quenches. We perform a detailed analysis of the probability of QPs produced at the two sites and the nature of the QPs in various phases, and obtain interesting results. More specifically, we find partial reflection of these QPs at the defect center or the site of h-quench, resulting in new timescales which have never been reported before.

Fidelity susceptibility and Loschmidt echo for generic paths in a three-spin interacting transverse Ising model

Abstract: We study the effect of the presence of different types of critical points, such as ordinary critical points, multicritical points and quasicritical points, along different paths on the fidelity susceptibility and Loschmidt echo of a three-spin interacting transverse Ising chain using a method that does not involve the language of tensors. We find that the scaling of the fidelity susceptibility and Loschmidt echo with the system size at these special critical points of the model studied is in agreement with the known results, thus supporting our method.

Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling

Abstract: The authors show that when the operation of a quantum machine drives the working substance across a phase transition, its finite-time thermodynamics is universal.

Adiabatic dynamics in passage across quantum critical lines and gapless phases

Abstract: It is well known that the dynamics of a quantum system is always nonadiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system. To illustrate the general argument, we study the defect generation in the quantum critical dynamics of a spin-1/2 anisotropic quantum XY spin chain with three spin interactions and a linearly driven staggered magnetic field.

Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Abstract: This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding

Quantum Phase Transitions

Abstract: We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

A quantum Newton's cradle

Abstract: It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 87Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.