Related papers: Quantum variance for dihedral Maass forms
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
During recent years, exact solutions of position-dependent mass Schr\"odinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic methods or supersymmetric quantum…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Mat\'ern autocovariance in dimension $d>4$. When $d<4$ this is…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that…
We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $\theta$ variables and…
We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show…
We perform a canonical analysis of the system of 2d vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions which have been made by other authors. We present a…
This paper investigates the quadratic irrationals that arise as periodic points of the Gauss type shift associated to the odd continued fraction expansion. It is shown that these numbers, which we call O-reduced, when ordered by the length…
Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…
We investigate the gauge-independent Hamiltonian formulation and the anomalous Ward identities of a matter-induced 1+1-dimensional gravity theory invariant under Weyl transformations and area-preserving diffeomorphisms, and compare the…
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…