156 research outputs found
k-Essence, superluminal propagation, causality and emergent geometry
The k-essence theories admit in general the superluminal propagation of the
perturbations on classical backgrounds. We show that in spite of the
superluminal propagation the causal paradoxes do not arise in these theories
and in this respect they are not less safe than General Relativity.Comment: 34 pages, 5 figure
Factor copula models for item response data
Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data
Geometric Strategy for the Optimal Quantum Search
We explore quantum search from the geometric viewpoint of a complex
projective space , a space of rays. First, we show that the optimal quantum
search can be geometrically identified with the shortest path along the
geodesic joining a target state, an element of the computational basis, and
such an initial state as overlaps equally, up to phases, with all the elements
of the computational basis. Second, we calculate the entanglement through the
algorithm for any number of qubits as the minimum Fubini-Study distance to
the submanifold formed by separable states in Segre embedding, and find that
entanglement is used almost maximally for large . The computational time
seems to be optimized by the dynamics as the geodesic, running across entangled
states away from the submanifold of separable states, rather than the amount of
entanglement itself.Comment: revtex, 10 pages, 7 eps figures, uses psfrag packag
A study of generalized second law of thermodynamics in modified f(R) Horava-Lifshitz gravity
This work investigates the validity of the generalized second law of
thermodynamics in modified f(R) Horava-Lifshitz gravity proposed by Chaichian
et al (2010) [Class. Quantum Grav. 27 (2010) 185021], which is invariant under
foliation-preserving diffeomorphisms. It has been observed that the equation of
state parameter behaves like quintessence (w > -1). We study the thermodynamics
of the apparent, event and particle horizons in this modified gravity. We
observe that under this gravity, the time derivative of total entropy stays at
positive level and hence the generalized second law is validated.Comment: 12 pages, 8 figures, Accepted for publication Astrophysics and Space
Science, 201
Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes
We construct and analyze a large class of exact five- and six-dimensional
regular and static solutions of the vacuum Einstein equations. These solutions
describe sequences of Kaluza-Klein bubbles and black holes, placed alternately
so that the black holes are held apart by the bubbles. Asymptotically the
solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they
are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In
particular, they occupy a hitherto unexplored region of the phase diagram,
since their relative tension exceeds that of the uniform black string. The
solutions contain bubbles and black holes of various topologies, including
six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology
S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against
gravitational collapse. We find two maps between solutions, one that relates
five- and six-dimensional solutions, and another that relates solutions in the
same dimension by interchanging bubbles and black holes. To illustrate the
richness of the phase structure and the non-uniqueness in the (\mu,n) phase
diagram, we consider in detail particular examples of the general class of
solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.
Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons
The stability of cosmological event and Cauchy horizons of spacetimes
associated with plane symmetric domain walls are studied. It is found that both
horizons are not stable against perturbations of null fluids and massless
scalar fields; they are turned into curvature singularities. These
singularities are light-like and strong in the sense that both the tidal forces
and distortions acting on test particles become unbounded when theses
singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques
Force and Motion Generation of Molecular Motors: A Generic Description
We review the properties of biological motor proteins which move along linear
filaments that are polar and periodic. The physics of the operation of such
motors can be described by simple stochastic models which are coupled to a
chemical reaction. We analyze the essential features of force and motion
generation and discuss the general properties of single motors in the framework
of two-state models. Systems which contain large numbers of motors such as
muscles and flagella motivate the study of many interacting motors within the
framework of simple models. In this case, collective effects can lead to new
types of behaviors such as dynamic instabilities of the steady states and
oscillatory motion.Comment: 29 pages, 9 figure
A Unified Algebraic Approach to Few and Many-Body Correlated Systems
The present article is an extended version of the paper {\it Phys. Rev.} {\bf
B 59}, R2490 (1999), where, we have established the equivalence of the
Calogero-Sutherland model to decoupled oscillators. Here, we first employ the
same approach for finding the eigenstates of a large class of Hamiltonians,
dealing with correlated systems. A number of few and many-body interacting
models are studied and the relationship between their respective Hilbert
spaces, with that of oscillators, is found. This connection is then used to
obtain the spectrum generating algebras for these systems and make an algebraic
statement about correlated systems. The procedure to generate new solvable
interacting models is outlined. We then point out the inadequacies of the
present technique and make use of a novel method for solving linear
differential equations to diagonalize the Sutherland model and establish a
precise connection between this correlated system's wave functions, with those
of the free particles on a circle. In the process, we obtain a new expression
for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having
Laughlin wave function as the ground-state and point out the natural emergence
of the underlying linear symmetry in this approach.Comment: 18 pages, Revtex format, To appear in Physical Review
Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
In this article we consider the zeta regularized determinant of Laplace-type
operators on the generalized cone. For {\it arbitrary} self-adjoint extensions
of a matrix of singular ordinary differential operators modelled on the
generalized cone, a closed expression for the determinant is given. The result
involves a determinant of an endomorphism of a finite-dimensional vector space,
the endomorphism encoding the self-adjoint extension chosen. For particular
examples, like the Friedrich's extension, the answer is easily extracted from
the general result. In combination with \cite{BKD}, a closed expression for the
determinant of an arbitrary self-adjoint extension of the full Laplace-type
operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic
Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds
Real-time anomalous fermion number violation is investigated for massless
chiral fermions in spherically symmetric SU(2) Yang-Mills gauge field
backgrounds which can be weakly dissipative or even nondissipative. Restricting
consideration to spherically symmetric fermion fields, the zero-eigenvalue
equation of the time-dependent effective Dirac Hamiltonian is studied in
detail. For generic spherically symmetric SU(2) gauge fields in Minkowski
spacetime, a relation is presented between the spectral flow and two
characteristics of the background gauge field. These characteristics are the
well-known ``winding factor,'' which is defined to be the change of the
Chern-Simons number of the associated vacuum sector of the background gauge
field, and a new ``twist factor,'' which can be obtained from the
zero-eigenvalue equation of the effective Dirac Hamiltonian but is entirely
determined by the background gauge field. For a particular class of (weakly
dissipative) Luscher-Schechter gauge field solutions, the level crossings are
calculated directly and nontrivial contributions to the spectral flow from both
the winding factor and the twist factor are observed. The general result for
the spectral flow may be relevant to electroweak baryon number violation in the
early universe.Comment: REVTeX, 43 pages, v4: final versio
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