25 research outputs found
Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl
J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian
augmented by a non-Hermitian -symmetric part, is re-examined in the
light of an su(1,1) approach. An alternative derivation, only relying on
properties of su(1,1) generators, is proposed. Being independent of the
realization considered for the latter, it opens the way towards the
construction of generalized non-Hermitian (not necessarily -symmetric)
oscillator Hamiltonians related by similarity to Hermitian ones. Some examples
of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5;
final published versio
Moyal products -- a new perspective on quasi-hermitian quantum mechanics
The rationale for introducing non-hermitian Hamiltonians and other
observables is reviewed and open issues identified. We present a new approach
based on Moyal products to compute the metric for quasi-hermitian systems. This
approach is not only an efficient method of computation, but also suggests a
new perspective on quasi-hermitian quantum mechanics which invites further
exploration. In particular, we present some first results which link the Berry
connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of
Non-Hermitian Operator
Boson-fermion mappings for odd systems from supercoherent states
We extend the formalism whereby boson mappings can be derived from
generalized coherent states to boson-fermion mappings for systems with an odd
number of fermions. This is accomplished by constructing supercoherent states
in terms of both complex and Grassmann variables. In addition to a known
mapping for the full so(2+1) algebra, we also uncover some other formal
mappings, together with mappings relevant to collective subspaces.Comment: 40 pages, REVTE
Bosonization in d=2 from finite chiral determinants with a Gauss decomposition
We show how to bosonize two-dimensional non-abelian models using finite
chiral determinants calculated from a Gauss decomposition. The calculation is
quite straightforward and hardly more involved than for the abelian case. In
particular, the counterterm , which is normally motivated from gauge
invariance and then added by hand, appears naturally in this approach.Comment: 4 pages, Revte
Loosely bound hyperons in the SU(3) Skyrme model
Hyperon pairs bound in deuteron like states are obtained within the SU(3)
Skyrme model in agreement with general expectations from boson exchange models.
The central binding from the flavor symmetry breaking terms increases with the
strangeness contents of the interacting baryons whereas the kinetic non-linear
-model term fixes the spin and isospin of the bound pair. We give a
complete account of the interactions of octet baryons within the product
approximation to baryon number configurations.Comment: 35 pages REVTEX including 2 figs, with 3 further figs available on
request from [email protected] or from [email protected]
SI-94-TP3S2; STPHY-Th/94-
Non-Hermitian Hamiltonians of Lie algebraic type
We analyse a class of non-Hermitian Hamiltonians, which can be expressed
bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic
su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of
Lie algebraic type. Demanding a real spectrum and the existence of a well
defined metric, we systematically investigate the constraints these
requirements impose on the coupling constants of the model and the parameters
in the metric operator. We compute isospectral Hermitian counterparts for some
of the original non-Hermitian Hamiltonian. Alternatively we employ a
generalized Bogoliubov transformation, which allows to compute explicitly real
energy eigenvalue spectra for these type of Hamiltonians, together with their
eigenstates. We compare the two approaches.Comment: 27 page
Time evolution of non-Hermitian Hamiltonian systems
We provide time-evolution operators, gauge transformations and a perturbative
treatment for non-Hermitian Hamiltonian systems, which are explicitly
time-dependent. We determine various new equivalence pairs for Hermitian and
non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in
addition in some cases also invariant under PT-symmetry. In particular, for the
harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate
explicitly various transition amplitudes, for the situation when these systems
are exposed to a monochromatic linearly polarized electric field.Comment: 25 pages Latex, 1 eps figure, references adde
Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
Witten's non-relativistic formalism of supersymmetric quantum mechanics was
based on a factorization and partnership between Schroedinger equations. We
show how it accommodates a transition to the partnership between relativistic
Klein-Gordon equations. In such a class of models the requirement of
supersymmetry is shown to lead to a certain "exceptional-point" instability of
ground states.Comment: 20 page
Nonperturbative flow equations from running expectation values
The original publication is available at http://prl.aps.org/abstract/PRL/v91/i8/e080602We show that Wegner’s flow equations, as recently discussed in the Lipkin model, can be solved selfconsistently.
This leads to a nonlinear differential equation which fully determines the order parameter
as a function of the dimensionless coupling constant, even across the phase transition. Since we consider
an expansion in the fluctuations, rather than the conventional expansion in the coupling constant,
convergence to the exact results is found in both phases when taking the thermodynamic limit.Publishers' versio