Related papers: Special functions from quantum canonical transform…
In this paper, we derive equations of motion for the normal-order, the symmetric-order and the antinormal-order quantum characteristic functions, applicable for general Hamiltonian systems. We do this by utilizing the `characteristic form'…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
The main goal of this thesis is to quantize the Einstein-Hilbert action extended by the quadratic curvature terms within the canonical quantization approach, thus formulating quantum geometrodynamics of the higher derivative theories. The…
Using the Madelung transformation on a generalized scalar Gross-Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete…
Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…
Motivated by the new Laplace transforms for the Kummer's confluent hypergeometric functions $_1F_1$ obtained recently by Kim et al. [Math $\&$ Comput. Modelling, 55 (2012), pp. 1068--1071], the authors aim is to establish so far unknown…
Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking…
A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a ``canonical basis'' for every…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
The Ashtekar variables have been use to find a number of exact solutions in quantum gravity and quantum cosmology. We investigate the origin of these solutions in the context of a number of canonical transformations (both complex and real)…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…