Smooth Quenches Research Articles

Scrambling under quench

We evaluate out of time ordered correlators in certain low dimensional quantum systems at zero temperature, subjected to homogenous quantum quenches. We find that when the Lyapunov exponent exists, it can be identified with the quenched energy. We show that the exponent naturally gets related to the post-quench effective temperature. In the context of sudden quenches the exponent is determined in terms of the quench amplitude while for smooth quenches we observe scalings (both the Kibble-Zurek as well as the fast) of the exponent with the quench rate. The scalings are identical to that of the energy generated during the quench.

Dynamics of logarithmic negativity and mutual information in smooth quenches

Abstract We study the time evolution of mutual information (MI) and logarithmic negativity (LN) in two-dimensional free scalar theory with two kinds of time-dependent masses: one time evolves continuously from non-zero mass to zero; the other time evolves continuously from finite mass to finite mass, but becomes massless once during the time evolution. We call the former protocol ECP, and the latter protocol CCP. Through numerical computation, we find that the time evolution of MI and LN in ECP follows a quasi-particle picture except for their late-time evolution, whereas that in CCP oscillates. Moreover, we find a qualitative difference between MI and LN which has not been known so far: MI in ECP depends on the slowly moving modes, but LN does not.

Thermohydraulic analysis of Tore Supra/WEST TF coil quench: Associated smooth quench occurrence in tokamak

The Toroidal Field (TF) system of the Tore Supra/WEST tokamak comprises 18 NbTi superconducting coils, cooled by a static superfluid helium bath at 1.8 K and carrying a nominal current of 1255 A. The 19th December 2017, at the end of plasma run #52205, a quench of TFC-09 was detected first on a secondary thermohydraulical signal (helium liquid level) and triggered the current Fast Safety Discharge (FSD). A numerical model of this quench has been developed with SuperMagnet (CryoSoft). The whole TFC-09 circular coil is modelled by THEA as a single large Cable-In-Conduit Conductor (CICC) with 2028 large rectangular strands (monolithic conductors of length equal to coil average perimeter). The external quench helium relief circuit (cold and warm safety valves, rupture disk and magnetic valve with corresponding pressure set) is modelled by FLOWER.The helium pressure in the coil, upstream of the cold safety valve (maximum value of 9 bar), and the expulsed helium temperature have been used as comparison between measurements and calculations which depend on the Minimum Quench Energy (MQE) used in THEA with small initial heat deposition length (few tens of centimeters) at low field region (external leg). This energy, in the order of few kJ, is compared to the real shape and energy of neutron and gamma flux caused by highly energetic runaway electrons colliding the outboard plasma facing components and which induced the quench. The expulsed helium mass flow rate of nearly 6 kg/s during 5 s has also been calculated. This event confirms on one hand the criticality and the possible occurrence of a so called “smooth quench” caused by small initial heat deposition length and at low field region and on the other hand the important interest of secondary quench detection which can be useful for other tokamak magnets safe operation and protection.

On fast quenches and spinning correlators

We study global quantum quenches in a continuous field theoretic system with UV fixed point. Assuming that the characteristic inverse time scale of the smooth quench is much larger than all scales inherent to the system except for the UV-cutoff, we derive the universal scaling behavior of the two-point correlation functions associated with Dirac fields and spin-1 currents. We argue that in certain regimes our results can be recovered using the technique of operator product expansion.

Quantum quenches in the Luttinger model and its close relatives

A number of results on quantum quenches in the Luttinger and related models are surveyed with emphasis on post-quench correlations. For the Luttinger model and initial gaussian states, we discuss both sudden and smooth quenches of the interaction and the emergence of a steady state described by a generalized Gibbs ensemble. Comparisons between analytics and numerics, and the question of universality or lack thereof are also discussed. The relevance of the theoretical results to current and future experiments in the fields of ultracold atomic gases and mesoscopic systems of electrons is also briefly touched upon. Wherever possible, our approach is pedagogical and self-contained. This work is dedicated to the memory of our colleague Alejandro Muramatsu.

Smooth and fast versus instantaneous quenches in quantum field theory

We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale $\delta t$, and {\em instantaneous quenches}, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols remain distinct in the limit $\delta t \rightarrow 0$ because of the relation of the quench rate to the UV cut-off, i.e., $1/\delta t\ll\Lambda$ always holds in the fast smooth quenches while $1/\delta t\sim\Lambda$ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small $\delta t$, the correlator scales universally with $\delta t$, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on $\delta t$ drops out. The excess energy density is finite (for finite $m\delta t$) and scales in a universal fashion for all $d$. However, the scaling behaviour produces a divergent result in the limit $m\delta t \rightarrow 0$ for $d\ge4$, just as in an instantaneous quench, where it is UV divergent for $d \geq 4$. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions $\Delta > d/2$.

Defect Formation beyond Kibble-Zurek Mechanism and Holography

We study the dynamic after a smooth quench across a continuous transition from the disordered phase to the ordered phase. Based on scaling ideas, linear response and the spectrum of unstable modes, we develop a theoretical framework, valid for any second order phase transition, for the early-time evolution of the condensate in the broken phase. Our analysis unveils a novel period of non-adiabatic evolution after the system passes through the phase transition, where a parametrically large amount of coarsening occurs before a well-defined condensate forms. Our formalism predicts a rate of defect formation parametrically smaller than the Kibble-Zurek prediction and yields a criterion for the break-down of Kibble-Zurek scaling for sufficiently fast quenches. We numerically test our formalism for a thermal quench in a 2 + 1 dimensional holographic superfluid. These findings, of direct relevance in a broad range of fields including cold atom, condensed matter, statistical mechanism and cosmology, are an important step towards a more quantitative understanding of dynamical phase transitions.

Universal scaling in fast quantum quenches in conformal field theories.

We study the time evolution of a conformal field theory deformed by a relevant operator under a smooth but fast quantum quench which brings it to the conformal point. We argue that when the quench time scale δt is small compared to the scale set by the relevant coupling, the expectation value of the quenched operator scales universally as δλ/δt(2Δ-d), where δλ is the quench amplitude. This growth is further enhanced by a logarithmic factor in even dimensions. We present explicit results for free scalar and fermionic field theories, supported by an analytic understanding of the leading contribution for fast quenches. Our results suggest that this scaling result, first found in holography, is in fact quite general. Our considerations also show that this limit of fast smooth quenches is quite different from an instantaneous quench from one time-independent Hamiltonian to another, where the state at the time of the quench serves as an initial condition for subsequent evolution with the final Hamiltonian.

Excitation energy after a smooth quench in a Luttinger liquid

Low energy physics of quasi-one-dimensional ultracold atomic gases is often described by a gapless Luttinger liquid (LL). It is nowadays routine to manipulate these systems by changing their parameters in time but, no matter how slow the manipulation is, it must excite a gapless system. We study a smooth change of parameters of the LL (a smooth "quench") with a variable quench time and find that the excitation energy decays with an inverse power of the quench time. This universal exponent is -2 at zero temperature, and -1 for slow enough quenches at finite temperature. The smooth quench does not excite beyond the range of validity of the low energy LL description.

Nonequilibrium dynamics of coupled quantum systems

The nonequilibrium dynamics of coupled quantum oscillators subject to different time-dependent quenches are analyzed in the context of the Liouville–von Neumann approach. We consider models of quantum oscillators in interaction that are exactly soluble in the cases of both sudden and smooth quenches. The time evolution of number densities, the final equilibration temperature and equilibration time for the problem of a quantum oscillator coupled to an infinity set of other oscillators (a bath) are explicitly worked out.

Nonequilibrium quantum dynamics of second order phase transitions

We use the so-called Liouville-von Neumann (LvN) approach to study the nonequilibrium quantum dynamics of time-dependent second order phase transitions. The LvN approach is a canonical method that unifies the functional Schr\"{o}dinger equation for the quantum evolution of pure states and the LvN equation for the quantum description of mixed states of either equilibrium or nonequilibrium. As nonequilibrium quantum mechanical systems we study a time-dependent harmonic and an anharmonic oscillator and find the exact Fock space and density operator for the harmonic oscillator and the nonperturbative Gaussian Fock space and density operator for the anharmonic oscillator. The density matrix and the coherent, thermal and coherent-thermal states are found in terms of their classical solutions, for which the effective Hamiltonians and equations of motion are derived. The LvN approach is further extended to quantum fields undergoing time-dependent second order phase transitions. We study an exactly solvable model with a finite smooth quench and find the two-point correlation functions. Due to the spinodal instability of long wavelength modes the two-point correlation functions lead to the $t^{1/4}$-scaling relation during the quench and the Cahn-Allen scaling relation $t^{1/2}$ after the completion of quench. Further, after the finite quench the domain formation shows a time-lag behavior at the cubic power of quench period. Finally we study the time-dependent phase transition of a self-interacting scalar field.