2,770 research outputs found
Ground-state properties of hard-core bosons confined on one-dimensional optical lattices
We study the ground-state properties of hard-core bosons trapped by arbitrary
confining potentials on one-dimensional optical lattices. A recently developed
exact approach based on the Jordan-Wigner transformation is used. We analyze
the large distance behavior of the one-particle density matrix, the momentum
distribution function, and the lowest natural orbitals. In addition, the
low-density limit in the lattice is studied systematically, and the results
obtained compared with the ones known for the hard-core boson gas without the
lattice.Comment: RevTex file, 14 pages, 22 figures, published versio
Entropy and Correlation Functions of a Driven Quantum Spin Chain
We present an exact solution for a quantum spin chain driven through its
critical points. Our approach is based on a many-body generalization of the
Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The
resulting nonequilibrium state of the system, while being a pure quantum state,
has local properties of a mixed state characterized by finite entropy density
associated with Kibble-Zurek defects. The entropy, as well as the finite spin
correlation length, are functions of the rate of sweep through the critical
point. We analyze the anisotropic XY spin 1/2 model evolved with a full
many-body evolution operator. With the help of Toeplitz determinants calculus,
we obtain an exact form of correlation functions. The properties of the evolved
system undergo an abrupt change at a certain critical sweep rate, signaling
formation of ordered domains. We link this phenomenon to the behavior of
complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg
Spectrum of the three dimensional fuzzy well
We develop the formalism of quantum mechanics on three dimensional fuzzy
space and solve the Schr\"odinger equation for a free particle, finite and
infinite fuzzy wells. We show that all results reduce to the appropriate
commutative limits. A high energy cut-off is found for the free particle
spectrum, which also results in the modification of the high energy dispersion
relation. An ultra-violet/infra-red duality is manifest in the free particle
spectrum. The finite well also has an upper bound on the possible energy
eigenvalues. The phase shifts due to scattering around the finite fuzzy
potential well have been calculated
Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator
It is shown that the local axial anomaly in dimensions emerges naturally
if one postulates an underlying noncommutative fuzzy structure of spacetime .
In particular the Dirac-Ginsparg-Wilson relation on is shown to
contain an edge effect which corresponds precisely to the ``fuzzy''
axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant
expansion of the quark propagator in the form where
is the lattice spacing on , is
the covariant noncommutative chirality and is an effective
Dirac operator which has essentially the same IR spectrum as
but differes from it on the UV modes. Most remarkably is the fact that both
operators share the same limit and thus the above covariant expansion is not
available in the continuum theory . The first bit in this expansion
although it vanishes as it stands in the continuum
limit, its contribution to the anomaly is exactly the canonical theta term. The
contribution of the propagator is on the other hand
equal to the toplogical Chern-Simons action which in two dimensions vanishes
identically .Comment: 26 pages, latex fil
Spin Chains as Perfect Quantum State Mirrors
Quantum information transfer is an important part of quantum information
processing. Several proposals for quantum information transfer along linear
arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect
transfer was shown to exist in two models with specifically designed strongly
inhomogeneous couplings. We show that perfect transfer occurs in an entire
class of chains, including systems whose nearest-neighbor couplings vary only
weakly along the chain. The key to these observations is the Jordan-Wigner
mapping of spins to noninteracting lattice fermions which display perfectly
periodic dynamics if the single-particle energy spectrum is appropriate. After
a half-period of that dynamics any state is transformed into its mirror image
with respect to the center of the chain. The absence of fermion interactions
preserves these features at arbitrary temperature and allows for the transfer
of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the
text, one new reference. Accepted by Phys. Rev. A (Rapid Communications
How to make a traversable wormhole from a Schwarzschild black hole
The theoretical construction of a traversable wormhole from a Schwarzschild
black hole is described, using analytic solutions in Einstein gravity. The
matter model is pure phantom radiation (pure radiation with negative energy
density) and the idealization of impulsive radiation is employed.Comment: 4 pages, 4 figure
Gravitating magnetic monopole in Vaidya geometry
A magnetic-monopole solution of a non-Abelian gauge theory as proposed by 't
Hooft and Polyakov is studied in the Vaidya spacetime. We find that the
solutions of Einstein equations generates a geometry of the Bonnor-Vaidya
corresponding to magnetically charged null fluid with Higgs field contributing
a cosmological term. In the absence of the scalar fields the corresponding
Wu-Yang solution of the gauge theory still generates the Bonnor-Vaidya
geometry, but with no cosmological term.Comment: 5 RevTeX pages, no figures, minor changes, to appear in Physical
Review
Non-adiabatic radiative collapse of a relativistic star under different initial conditions
We examine the role of space-time geometry in the non-adiabatic collapse of a
star dissipating energy in the form of radial heat flow, studying its evolution
under different initial conditions. The collapse of a star with interior
comprising of a homogeneous perfect fluid is compared with that of a star
filled with inhomogeneous imperfect fluid with anisotropic pressure. Both the
configurations are spherically symmetric, however, in the latter case, the
physical space of the configurations is assumed to be
inhomogeneous endowed with spheroidal or pseudo-spheroidal geometry. It is
observed that as long as the collapse is shear-free, its evolution depends only
on the mass and size of the star at the onset of collapse.Comment: To appear in Pramana- j. of physic
Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes
We study scalar field and electromagnetic perturbations on Locally
Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently
developed covariant and gauge-invariant perturbation formalism. From the
Klein-Gordon equation and Maxwell's equations, respectively, we derive
covariant and gauge-invariant wave equations for the perturbation variables and
thereby find the generalised Regge-Wheeler equations for these LRS class II
spacetime perturbations. As illustrative examples, the results are discussed in
detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes
of dust Universes.Comment: 22 pages; v3 has minor changes to match published versio
Kerr-Schild Symmetries
We study continuous groups of generalized Kerr-Schild transformations and the
vector fields that generate them in any n-dimensional manifold with a
Lorentzian metric. We prove that all these vector fields can be intrinsically
characterized and that they constitute a Lie algebra if the null deformation
direction is fixed. The properties of these Lie algebras are briefly analyzed
and we show that they are generically finite-dimensional but that they may have
infinite dimension in some relevant situations. The most general vector fields
of the above type are explicitly constructed for the following cases: any
two-dimensional metric, the general spherically symmetric metric and
deformation direction, and the flat metric with parallel or cylindrical
deformation directions.Comment: 15 pages, no figures, LaTe
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