2,431 research outputs found
Impurity and boundary effects in one and two-dimensional inhomogeneous Heisenberg antiferromagnets
We calculate the ground-state energy of one and two-dimensional spatially
inhomogeneous antiferromagnetic Heisenberg models for spins 1/2, 1, 3/2 and 2.
Our calculations become possible as a consequence of the recent formulation of
density-functional theory for Heisenberg models. The method is similar to
spin-density-functional theory, but employs a local-density-type approximation
designed specifically for the Heisenberg model, allowing us to explore
parameter regimes that are hard to access by traditional methods, and to
consider complications that are important specifically for nanomagnetic
devices, such as the effects of impurities, finite-size, and boundary geometry,
in chains, ladders, and higher-dimensional systems.Comment: 4 pages, 4 figures, accepted by Phys. Rev.
Pseudo-Hermitian Representation of Quantum Mechanics
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used
to define a unitary quantum system, if one modifies the inner product of the
Hilbert space properly. We give a comprehensive and essentially self-contained
review of the basic ideas and techniques responsible for the recent
developments in this subject. We provide a critical assessment of the role of
the geometry of the Hilbert space in conventional quantum mechanics to reveal
the basic physical principle motivating our study. We then offer a survey of
the necessary mathematical tools and elaborate on a number of relevant issues
of fundamental importance. In particular, we discuss the role of the antilinear
symmetries such as PT, the true meaning and significance of the charge
operators C and the CPT-inner products, the nature of the physical observables,
the equivalent description of such models using ordinary Hermitian quantum
mechanics, the pertaining duality between local-non-Hermitian versus
nonlocal-Hermitian descriptions of their dynamics, the corresponding classical
systems, the pseudo-Hermitian canonical quantization scheme, various methods of
calculating the (pseudo-) metric operators, subtleties of dealing with
time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation
of the theory, and the structure of the state space and its ramifications for
the quantum Brachistochrone problem. We also explore some concrete physical
applications of the abstract concepts and tools that have been developed in the
course of this investigation. These include applications in nuclear physics,
condensed matter physics, relativistic quantum mechanics and quantum field
theory, quantum cosmology, electromagnetic wave propagation, open quantum
systems, magnetohydrodynamics, quantum chaos, and biophysics.Comment: 76 pages, 2 figures, 243 references, published as Int. J. Geom. Meth.
Mod. Phys. 7, 1191-1306 (2010
Metric operators for non-Hermitian quadratic su(2) Hamiltonians
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear
symmetry is constructed. This is achieved by analysing the possible symmetries
of such systems in terms of automorphisms of the algebra. In fact, different
realisations for this type of symmetry are obtained, including the natural
occurrence of charge conjugation together with parity and time reversal. Once
specified the underlying anti-linear symmetry of the Hamiltonian, the former,
if unbroken, leads to a purely real spectrum and the latter can be mapped to a
Hermitian counterpart by, amongst other possibilities, a similarity
transformation. Here, Lie-algebraic methods which were used to investigate the
generalised Swanson Hamiltonian are employed to identify the class of quadratic
Hamiltonians that allow for such a mapping to the Hermitian counterpart.
Whereas for the linear su(2) system every Hamiltonian of this type can be
mapped to a Hermitian counterpart by a transformation which is itself an
exponential of a linear combination of su(2) generators, the situation is more
complicated for quadratic Hamiltonians. Therefore, the possibility of more
elaborate similarity transformations, including quadratic exponents, is also
explored in detail. The existence of finite dimensional representations for the
su(2) Hamiltonian, as opposed to the su(1,1) studied before, allows for
comparison with explicit diagonalisation results for finite matrices. Finally,
the similarity transformations constructed are compared with the analogue of
Swanson's method for exact diagonalsation of the problem, establishing a simple
relation between both approaches.Comment: 25 pages, 6 figure
Estrutura do dossel em pastagens de capim-marandu submetidas a quatro ofertas de lâminas foliares.
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Previous issue date: 2008-01-1
The Pauli equation with complex boundary conditions
We consider one-dimensional Pauli Hamiltonians in a bounded interval with
possibly non-self-adjoint Robin-type boundary conditions. We study the
influence of the spin-magnetic interaction on the interplay between the type of
boundary conditions and the spectrum. A special attention is paid to
PT-symmetric boundary conditions with the physical choice of the time-reversal
operator T.Comment: 16 pages, 4 figure
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
A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field
We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turns out to be unique with the sole assumption that the Dyson map is Hermitian. Finally we compute the magnetization of the chain in the z and x direction
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