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Finite-size error (FSE), the discrepancy between an observable in a finite system and in the thermodynamic limit, is ubiquitous in numerical simulations of quantum many body systems. Although a rough estimate of these errors can be obtained…

All energy measurements of a quantum system are prone to inaccuracies. In particular, if such measurements are carried over a finite period of time the accuracy of the result is affected by the length of that period. Here I show an upper…

In this paper the local singularities of integrable Hamiltonian systems with two degrees of freedom are studied. The topological obstruction to the existence of focus-focus singularity with given complexity was found. It has been showed…

A finite-difference time-domain (FDTD) modelling of finite-size zero thickness space-time modulated Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and numerically demonstrated. A typical…

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…

In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…

In Monte Carlo simulations of lattice field theory with a $\theta$ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution $P(Q)$.…

Over the last few years it was pointed out that certain observables of time-evolving quantum systems may have singularities at certain moments in time, mimicking the singularities physical systems have when undergoing phase transitions.…

This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…

We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…

We establish robust exponential convergence for $rp$-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{balanced norm} which is stronger than the usual energy norm associated with…

Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that…

We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas…

We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry…

This work investigates a mathematical model arising in the study of MEMS devices, described by the following parabolic equation on $[0,T)\times\Omega$: $$\partial_t v = \Delta v + \frac{\lambda}{(1-v)^2\left( 1 + \gamma \int_{\Omega}…

We report on low temperature measurements performed on micro-electro-mechanical systems (MEMS) driven deeply into the non-linear regime. The materials are kept in their elastic domain, while the observed non-linearity is purely of…

This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…

We consider a nonlocal parabolic model for a micro-electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a…

We derive generic upper bounds on the rate of purity change and entropy increase for open quantum systems. These bounds depend solely on the generators of the nonunitary dynamics and are independent of the particular states of the systems.…