Latest Papers in Condensed Matter Physics

Statistical Mechanics

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Closed-form expression for cross-channel conformal blocks near the lightcone (1906.00707v2)

Wenliang Li

2019-06-03

In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalars. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampe de Feriet function, which applies to intermediate states of arbitrary spin in general dimensions. We also derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our approach and results may shed light on the complete analytic structure of conformal blocks.

Out of time ordered effective dynamics of a quartic oscillator (1905.08307v4)

Bidisha Chakrabarty, Soumyadeep Chaudhuri

2019-05-20

We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle.

Dynamical topological quantum phase transitions in nonintegrable models (1904.00867v2)

I. Hagymási, C. Hubig, Ö. Legeza, U. Schollwöck

2019-04-01

We consider sudden quenches across quantum phase transitions in the XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.

A note on the metastability in three modifications of the standard Ising model (1705.07012v2)

Kaveh Bashiri

2017-05-19

We consider three extensions of the standard 2D Ising model with Glauber dynamics on a finite torus at low temperature. The first model is an anisotropic version, where the interaction energy takes different values on vertical and on horizontal bonds. The second model adds next-nearest-neighbor attraction to the standard Ising model. And the third model associates different alternating signs for the magnetic fields on even and odd rows. All these models have already been studied, and results concerning metastability have been established using the so-called pathwise approach. In this text, we extend these earlier results, and apply the potential-theoretic approach to metastability to obtain more precise asymptotic information on the transition time from the metastable phase to the stable phase.

Measurement of Anomalous Diffusion Using Recurrent Neural Networks (1905.02038v2)

Stefano Bo, Falko Schmidt, Ralf Eichhorn, Giovanni Volpe

2019-05-06

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently characterize anomalous diffusion by determining the exponent from a single short trajectory, outperforming the standard estimation based on the MSD when the available data points are limited, as is often the case in experiments. Furthermore, the RNN can handle more complex tasks where there are no standard approaches, such as determining the anomalous diffusion exponent from a trajectory sampled at irregular times, and estimating the switching time and anomalous diffusion exponents of an intermittent system that switches between different kinds of anomalous diffusion. We validate our method on experimental data obtained from sub-diffusive colloids trapped in speckle light fields and super-diffusive microswimmers.

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