Related papers: Six-dimensional space-time from quaternionic quant…

The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…

We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics…

Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…

A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without…

The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms…

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…

The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or…

A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained…

For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise…

We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial…

We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…

We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our…

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The…

The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…

We introduce a complete gauge fixing for cylindrical spacetimes in vacuo that, in principle, do not contain the axis of symmetry. By cylindrically symmetric we understand spacetimes that possess two commuting spacelike Killing vectors, one…

We explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology, by identifying those variables for the description of the…

An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian…

We propose a (theoretical ;-) model for quantum computation where the result can be read out from the time average of the Hamiltonian dynamics of a 2-dimensional crystal on a cylinder. The Hamiltonian is a spatially local interaction among…

We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…