675 research outputs found
On dynamical tunneling and classical resonances
This work establishes a firm relationship between classical nonlinear
resonances and the phenomenon of dynamical tunneling. It is shown that the
classical phase space with its hierarchy of resonance islands completely
characterizes dynamical tunneling and explicit forms of the dynamical barriers
can be obtained only by identifying the key resonances. Relationship between
the phase space viewpoint and the quantum mechanical superexchange approach is
discussed in near-integrable and mixed regular-chaotic situations. For
near-integrable systems with sufficient anharmonicity the effect of multiple
resonances {\it i.e.,} resonance-assisted tunneling can be incorporated
approximately. It is also argued that the, presumed, relation of avoided
crossings to nonlinear resonances does not have to be invoked in order to
understand dynamical tunneling. For molecules with low density of states the
resonance-assisted mechanism is expected to be dominant.Comment: Completely rewritten and expanded version of a previous submission
physics/0410033. 14 pages and 10 figure
Sequential measurement of conjugate variables as an alternative quantum state tomography
It is shown how it is possible to reconstruct the initial state of a
one-dimensional system by measuring sequentially two conjugate variables. The
procedure relies on the quasi-characteristic function, the Fourier-transform of
the Wigner quasi-probability. The proper characteristic function obtained by
Fourier-transforming the experimentally accessible joint probability of
observing "position" then "momentum" (or vice versa) can be expressed as a
product of the quasi-characteristic function of the two detectors and that,
unknown, of the quantum system. This allows state reconstruction through the
sequence: data collection, Fourier-transform, algebraic operation, inverse
Fourier-transform. The strength of the measurement should be intermediate for
the procedure to work.Comment: v2, 5 pages, no figures, substantial improvements in the
presentation, thanks to an anonymous referee. v3, close to published versio
Symmetry of Quantum Phase Space in a Degenerate Hamiltonian System
Using Husimi function approach, we study the ``quantum phase space'' of a
harmonic oscillator interacting with a plane monochromatic wave. We show that
in the regime of weak chaos, the quantum system has the same symmetry as the
classical system. Analytical results agree with the results of numerical
calculations.Comment: 11 pages LaTex, including 2 Postscript figure
A set of exactly solvable Ising models with half-odd-integer spin
We present a set of exactly solvable Ising models, with half-odd-integer
spin-S on a square-type lattice including a quartic interaction term in the
Hamiltonian. The particular properties of the mixed lattice, associated with
mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction,
allow us to map this system either onto a purely spin-1/2 lattice or onto a
purely spin-S lattice. By imposing the condition that the mixed
half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a
set of exact solutions that satisfy the {\it free fermion} condition of the
eight vertex model. The number of solutions for a general half-odd-integer
spin-S is given by . Therefore we conclude that this transformation is
equivalent to a simple spin transformation which is independent of the
coordination number
Understanding highly excited states via parametric variations
Highly excited vibrational states of an isolated molecule encode the
vibrational energy flow pathways in the molecule. Recent studies have had
spectacular success in understanding the nature of the excited states mainly
due to the extensive studies of the classical phase space structures and their
bifurcations. Such detailed classical-quantum correspondence studies are
presently limited to two or quasi two dimensional systems. One of the main
reasons for such a constraint has to do with the problem of visualization of
relevant objects like surface of sections and Wigner or Husimi distributions
associated with an eigenstate. This neccesiates various alternative techniques
which are more algebraic than geometric in nature. In this work we introduce
one such method based on parametric variation of the eigenvalues of a
Hamiltonian. It is shown that the level velocities are correlated with the
phase space nature of the corresponding eigenstates. A semiclassical expression
for the level velocities of a single resonance Hamiltonian is derived which
provides theoretical support for the correlation. We use the level velocities
to dynamically assign the highly excited states of a model spectroscopic
Hamiltonian in the mixed phase space regime. The effect of bifurcations on the
level velocities is briefly discussed using a recently proposed spectroscopic
Hamiltonian for the HCP molecule.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy
Orthomodular-Valued Models for Quantum Set Theory
In 1981, Takeuti introduced quantum set theory by constructing a model of set
theory based on quantum logic represented by the lattice of closed linear
subspaces of a Hilbert space in a manner analogous to Boolean-valued models of
set theory, and showed that appropriate counterparts of the axioms of
Zermelo-Fraenkel set theory with the axiom of choice (ZFC) hold in the model.
In this paper, we aim at unifying Takeuti's model with Boolean-valued models by
constructing models based on general complete orthomodular lattices, and
generalizing the transfer principle in Boolean-valued models, which asserts
that every theorem in ZFC set theory holds in the models, to a general form
holding in every orthomodular-valued model. One of the central problems in this
program is the well-known arbitrariness in choosing a binary operation for
implication. To clarify what properties are required to obtain the generalized
transfer principle, we introduce a class of binary operations extending the
implication on Boolean logic, called generalized implications, including even
non-polynomially definable operations. We study the properties of those
operations in detail and show that all of them admit the generalized transfer
principle. Moreover, we determine all the polynomially definable operations for
which the generalized transfer principle holds. This result allows us to
abandon the Sasaki arrow originally assumed for Takeuti's model and leads to a
much more flexible approach to quantum set theory.Comment: 25 pages, v2: to appear in Rev. Symb. Logic, v3: corrected typo
Husimi coordinates of multipartite separable states
A parametrization of multipartite separable states in a finite-dimensional
Hilbert space is suggested. It is proved to be a diffeomorphism between the set
of zero-trace operators and the interior of the set of separable density
operators. The result is applicable to any tensor product decomposition of the
state space. An analytical criterion for separability of density operators is
established in terms of the boundedness of a sequence of operators.Comment: 19 pages, 1 figure, LaTe
Determination of Compton profiles at solid surfaces from first-principles calculations
Projected momentum distributions of electrons, i.e. Compton profiles above
the topmost atomic layer have recently become experimentally accessible by
kinetic electron emission in grazing-incidence scattering of atoms at
atomically flat single crystal metal surfaces. Sub-threshold emission by slow
projectiles was shown to be sensitive to high-momentum components of the local
Compton profile near the surface. We present a method to extract momentum
distribution, Compton profiles, and Wigner and Husimi phase space distributions
from ab-initio density-functional calculations of electronic structure. An
application for such distributions to scattering experiments is discussed.Comment: 13 pages, 5 figures, submitted to PR
Fisher information, Wehrl entropy, and Landau Diamagnetism
Using information theoretic quantities like the Wehrl entropy and Fisher's
information measure we study the thermodynamics of the problem leading to
Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic
field. It is shown that such a problem can be "translated" into that of the
thermal harmonic oscillator. We discover a new Fisher-uncertainty relation,
derived via the Cramer-Rao inequality, that involves phase space localization
and energy fluctuations.Comment: no figures. Physical Review B (2005) in pres
Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach
We investigate the triangular-lattice antiferromagnetic Ising model with a
spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was
first discussed by Kitatani and Oguchi. By employing the effective geometric
factor, we analyze the scaling dimensions of the operators around the
Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the
global phase diagram. Our numerical data exhibit that two types of
BKT-transition lines separate the intermediate critical region from the ordered
and disordered phases, and they do not merge into a single curve in the
antiferromagnetic region. We also estimate the central charge and perform some
consistency checks among scaling dimensions in order to provide the evidence of
the six-state clock universality. Further, we provide an analysis of the shapes
of boundaries based on the crossover argument.Comment: 8 pages, 5 figure
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