Related papers: Bosons Live in Symplectic Coset Spaces
The compact groups such as $SU(n)$ and $SO(n)$ groups have been heavily studied and applied in the study of quantum many body systems. However, the non-compact groups such as the real symplectic groups are less touched. In this paper, we…
We examine Borel subgroup orbits in the classical symmetric space of type CI, which are parametrized by skew symmetric (n, n)-clans. We describe bijections between such clans, certain weighted lattice paths, and pattern-avoiding signed…
The aim of this paper is to clarify the conceptual difference which exists between the interactions of composite bosons and the interactions of elementary bosons. A special focus is made on the physical processes which are missed when…
The permutation symmetry is a fundamental attribute of the collective wavefunction of indistinguishable particles. It makes a difference for the behavior of collective systems having different quantum statistics but existing in the same…
The symmetrization postulate asserts that the state of particular species of particles can only be of one permutation symmetry type: symmetric for bosons and antisymmetric for fermions. We report some experimental results showing that pairs…
Fundamental representations of real simple Poisson Lie groups are Poisson actions with a suitable choice of the Poisson structure on the underlying (real) vector space. We study these (mostly quadratic) Poisson structures and corresponding…
In this paper we show that the nontrivial fundamental group $\pi_1 SO(3) ={\Bbb Z}_2$ for the group SO(3) of global proper rotations of a four-dimensional Euclidian space (when a spin structure is introduced preliminarily in that space)…
Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably…
We study the quantum dynamics of conversion of composite bosons into fermionic fragment species with increasing densities of bound fermion pairs using the open quantum system approach. The Hilbert space of $N$-state-function is decomposed…
We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson…
A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on…
We prove two equilibrium properties of a system of interacting atoms in three or higher dimensional continuous space. (i) If the particles interact via pair potentials of a nonnegative Fourier transform, their self-organization into…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
The notion of representative statistical ensembles, correctly representing statistical systems, is strictly formulated. This notion allows for a proper description of statistical systems, avoiding inconsistencies in theory. As an…
Satyendra Nath Bose's attempt to describe the quantum statistical aspects of light consistently in terms of particles, and Einstein's generalisation, lead to the concept of Bosons as a class of quanta obeying `Bose-Einstein statistics'.…
In contrast to classical physics, quantum mechanics divides particles into two classes-bosons and fermions-whose exchange statistics dictate the dynamics of systems at a fundamental level. In two dimensions quasi-particles known as 'anyons'…
For a quantum system of N identical, harmonically interacting particles in a one-dimensional harmonic trap we calculate for the bosonic and fermionic ground state the corresponding 1-particle reduced density operator $\rho_1$ analytically.…
I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and…
Starting from considerations of Bosons at the real life Compton scale we go on to a description of Fermions, specifically the Dirac equation in terms of an underlying noncommutative geometry described by the Dirac $\gamma$ matrices and…