Related papers: A quantitative formula for the imaginary part of a…

We consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by computing which characters appear in the representation. This…

We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…

The gauge formulation of Einstein gravity in AdS$_3$ background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is…

A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…

Let $B=(B^{(1)},B^{(2)})$ be a two-dimensional fractional Brownian motion with Hurst index $\alpha\in (0,1/4)$. Using an analytic approximation $B(\eta)$ of $B$ introduced in \cite{Unt08}, we prove that the rescaled L\'evy area process…

Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[H, ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule.…

The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval…

Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional quasi-relativistic Hamiltonian (-h^2 c^2 d^2/dx^2 + m^2 c^4)^(1/2) + V_well(x) (the Klein-Gordon square-root operator with electrostatic potential) with the infinite…

Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $\Gamma < \mathrm{PSL}_2(\mathbf{R})$. We estimate the rate of decay of the coefficients in the expansion of $f_1\overline{f_2}$ in a Laplace eigenbasis.…

We consider the one-dimensional Schr\"odinger equation $-f''+q_\alpha f = Ef$ on the positive half-axis with the potential $q_\alpha(r)=(\alpha-1/4)r^{-2}$. It is known that the value $\alpha=0$ plays a special role in this problem: all…

We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…

On any Reflection Equation algebra corresponding to a skew-invertible Hecke symmetry (i.e. a special type solution of the Quantum Yang-Baxter Equation) we define analogs of the partial derivatives. Together with elements of the initial…

In this work, we first study the solvability of moment problems involving real exponentials and provide explicit estimates of the associated control cost. The result holds when the increasing sequence of distinct real numbers satisfies a…

We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…

Let $A_1$ be the (first) Weyl algebra, and let $G$ be its automorphism group. We study the natural action of $G$ on the space of isomorphism classes of right ideals of $A_1$ (equivalently, of finitely generated rank 1 torsion-free right…

We give a refined description of the dominant spectrum of a non-local operator that models growth and equal mitosis of cells. More precisely we look at the spectrum in half planes at the right hand side of the first accumulation point of…

Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…

We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…

We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems…

In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation…