19 research outputs found

### Parameter symmetries of quantum many-body systems

We analyze the occurrence of dynamically equivalent Hamiltonians in the
parameter space of general many-body interactions for quantum systems,
particularly those that conserve the total number of particles. As an
illustration of the general framework, the appearance of parameter symmetries
in the interacting boson model-1 and their absence in the Ginocchio SO(8)
fermionic model are discussed.Comment: 8 pages, REVTeX, no figur

### Second Virial Coefficient for Noncommutative Space

The second virial coefficient $B_{2}^{nc}(T)$ for non-interacting particles
moving in a two-dimensional noncommutative space and in the presence of a
uniform magnetic field $\vec B$ is presented. The noncommutativity parameter
\te can be chosen such that the $B_{2}^{nc}(T)$ can be interpreted as the
second virial coefficient for anyons of statistics \al in the presence of
$\vec B$ and living on the commuting plane. In particular in the high
temperature limit \be\lga 0, we establish a relation between the parameter
\te and the statistics \al. Moreover, $B_{2}^{nc}(T)$ can also be
interpreted in terms of composite fermions.Comment: 11 pages, misprints corrected and references adde

### CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C

A brief overview is given of recent developments and fresh ideas at the
intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric
quantum mechanics (SUSY QM). We study the consequences of the assumption that
the "charge" operator C is represented in a differential-operator form. Besides
the freedom allowed by the Hermiticity constraint for the operator CP,
encouraging results are obtained in the second-order case. The integrability of
intertwining relations proves to match the closure of nonlinear SUSY algebra.
In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial
oscillators with real spectrum which turn out to be PT-asymmetric.Comment: 25 page

### A Matrix Model for \nu_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States

We propose a matrix model to describe a class of fractional quantum Hall
(FQH) states for a system of (N_1+N_2) electrons with filling factor more
general than in the Laughlin case. Our model, which is developed for FQH states
with filling factor of the form \nu_{k_1k_2}=\frac{k_1+k_2}{k_1k_2} (k_1 and
k_2 odd integers), has a U(N_1)\times U(N_2) gauge invariance, assumes that FQH
fluids are composed of coupled branches of the Laughlin type, and uses ideas
borrowed from hierarchy scenarios. Interactions are carried, amongst others, by
fields in the bi-fundamentals of the gauge group. They simultaneously play the
role of a regulator, exactly as does the Polychronakos field. We build the
vacuum configurations for FQH states with filling factors given by the series
\nu_{p_1p_2}=\frac{p_2}{p_1p_2-1}, p_1 and p_2 integers. Electrons are
interpreted as a condensate of fractional D0-branes and the usual degeneracy of
the fundamental state is shown to be lifted by the non-commutative geometry
behaviour of the plane. The formalism is illustrated for the state at
\nu={2/5}.Comment: 40 pages, 1 figure, clarifications and references adde

### Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model

For a specific exactly solvable 2 by 2 matrix model with a PT-symmetric
Hamiltonian possessing a real spectrum, we construct all the eligible physical
metrics and show that none of them admits a factorization CP in terms of an
involutive charge operator C. Alternative ways of restricting the physical
metric to a unique form are briefly discussed.Comment: 13 page