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Quantum critical states exhibit strong quantum fluctuations and are therefore highly susceptible to perturbations. In this work we study the dynamical stability against a sudden coupling to these strong fluctuations by quenching the order…
In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase…
In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017}…
This paper proposes a novel Generalized Non-Standard Finite Difference (GNSFD) scheme for the numerical solution of a class of fractional partial differential equations (FrPDEs). The formulation of the method is grounded in optimization and…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
We investigate dynamical quantum phase transitions (DQPTs) in quantum systems that possess well-defined classical limits, focusing on the spinor Bose-Einstein condensate and the Lipkin-Meshkov-Glick model. We diagnose the DQPTs with the…
We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian…
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the…
A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes depending on the drive frequency. We compute the behavior of quantities…
The random matrix ensembles (RME) of quantum statistical Hamiltonians, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied in literature to following quantum statistical systems:…
Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct…
We study dynamical phase transitions (DPT) in the driven and damped Dicke model, realizable for example by a driven atomic ensemble collectively coupled to a damped cavity mode. These DPTs are characterized by non-analyticities of certain…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not…
One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum…
Accurate frequency estimation is critical for the control, monitoring and protection of electrical power systems, in particular, of systems with a high penetration of power electronics. This paper introduces the novel concept of Quasi…
We address the quantification of non-Gaussianity of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in details the properties and the relationships of two recently proposed…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
In this paper, we explore dimension reduction for functional time series. We propose a generalized dynamic functional principal component analysis (GDFPCA) which does not rely on spectral density estimation and demonstrates strong empirical…