284 research outputs found
Collective motions of a quantum gas confined in a harmonic trap
Single-component quantum gas confined in a harmonic potential, but otherwise
isolated, is considered. From the invariance of the system of the gas under a
displacement-type transformation, it is shown that the center of mass
oscillates along a classical trajectory of a harmonic oscillator. It is also
shown that this harmonic motion of the center has, in fact, been implied by
Kohn's theorem. If there is no interaction between the atoms of the gas, the
system in a time-independent isotropic potential of frequency is
invariant under a squeeze-type unitary transformation, which gives collective
{\it radial} breathing motion of frequency to the gas. The amplitudes
of the oscillating and breathing motions from the {\it exact} invariances could
be arbitrarily large. For a Fermi system, appearance of mode of the
large breathing motion indicates that there is no interaction between the
atoms, except for a possible long-range interaction through the
inverse-square-type potential.Comment: Typos in the printed verions are correcte
Coevolutionary dynamics on scale-free networks
We investigate Bak-Sneppen coevolution models on scale-free networks with
various degree exponents including random networks. For ,
the critical fitness value approaches to a nonzero finite value in the
limit , whereas approaches to zero as .
These results are explained by showing analytically on the networks with size . The avalanche size distribution
shows the normal power-law behavior for . In contrast,
for has two power-law regimes. One is a short regime for
small with a large exponent and the other is a long regime for
large with a small exponent (). The origin of the
two power-regimes is explained by the dynamics on an artificially-made
star-linked network.Comment: 5 pages, 5 figure
Coherent States and Geometric Phases in Calogero-Sutherland Model
Exact coherent states in the Calogero-Sutherland models (of time-dependent
parameters) which describe identical harmonic oscillators interacting through
inverse-square potentials are constructed, in terms of the classical solutions
of a harmonic oscillator. For quasi-periodic coherent states of the
time-periodic systems, geometric phases are evaluated. For the
Calogero-Sutherland model, the phase is calculated for a general coherent
state. The phases for other models are also considered.Comment: To appear in the Int. J. Mod. Phys.
Diffusive Capture Process on Complex Networks
We study the dynamical properties of a diffusing lamb captured by a diffusing
lion on the complex networks with various sizes of . We find that the life
time and the survival probability becomes finite on scale-free networks with degree exponent
. However, for has a long-living tail on
tree-structured scale-free networks and decays exponentially on looped
scale-free networks. It suggests that the second moment of degree distribution
kn(k)n(k)\sim k^{-\sigma}\gamma<3n(k)k\approx k_{max}n(k)n(k)\sim k^2P(k)N_{tot}, which
causes the dependent behavior of and $.Comment: 9 pages, 6 figure
`Operational' Energy Conditions
I show that a quantized Klein-Gordon field in Minkowski space obeys an
`operational' weak energy condition: the energy of an isolated device
constructed to measure or trap the energy in a region, plus the energy it
measures or traps, cannot be negative. There are good reasons for thinking that
similar results hold locally for linear quantum fields in curved space-times. A
thought experiment to measure energy density is analyzed in some detail, and
the operational positivity is clearly manifested.
If operational energy conditions do hold for quantum fields, then the
negative energy densities predicted by theory have a will-o'-the-wisp
character: any local attempt to verify a total negative energy density will be
self-defeating on account of quantum measurement difficulties. Similarly,
attempts to drive exotic effects (wormholes, violations of the second law,
etc.) by such densities may be defeated by quantum measurement problems. As an
example, I show that certain attempts to violate the Cosmic Censorship
principle by negative energy densities are defeated.
These quantum measurement limitations are investigated in some detail, and
are shown to indicate that space-time cannot be adequately modeled classically
in negative energy density regimes.Comment: 18 pages, plain Tex, IOP macros. Expanded treatment of measurement
problems for space-time, with implications for Cosmic Censorship as an
example. Accepted by Classical and Quantum Gravit
Dynamical surface structures in multi-particle-correlated surface growths
We investigate the scaling properties of the interface fluctuation width for
the -mer and -particle-correlated deposition-evaporation models. These
models are constrained with a global conservation law that the particle number
at each height is conserved modulo . In equilibrium, the stationary
roughness is anomalous but universal with roughness exponent ,
while the early time evolution shows nonuniversal behavior with growth exponent
varying with models and . Nonequilibrium surfaces display diverse
growing/stationary behavior. The -mer model shows a faceted structure, while
the -particle-correlated model a macroscopically grooved structure.Comment: 16 pages, 10 figures, revte
S matrix of collective field theory
By applying the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism, we
study the S matrix of collective field theory in which fermi energy is larger
than the height of potential. We consider the spatially symmetric and
antisymmetric boundary conditions. The difference is that S matrices are
proportional to momenta of external particles in antisymmetric boundary
condition, while they are proportional to energies in symmetric boundary
condition. To the order of , we find simple formulas for the S matrix
of general potential. As an application, we calculate the S matrix of a case
which has been conjectured to describe a "naked singularity".Comment: 19 page, LaTe
Geometric Phase, Hannay's Angle, and an Exact Action Variable
Canonical structure of a generalized time-periodic harmonic oscillator is
studied by finding the exact action variable (invariant). Hannay's angle is
defined if closed curves of constant action variables return to the same curves
in phase space after a time evolution. The condition for the existence of
Hannay's angle turns out to be identical to that for the existence of a
complete set of (quasi)periodic wave functions. Hannay's angle is calculated,
and it is shown that Berry's relation of semiclassical origin on geometric
phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version
Restrictions on negative energy density in a curved spacetime
Recently a restriction ("quantum inequality-type relation") on the
(renormalized) energy density measured by a static observer in a "globally
static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for
the minimally coupled scalar field, in the extension of quantum inequality-type
relation on flat spacetime of Ford and Roman. They found negative lower bounds
for the line integrals of energy density multiplied by a sampling (weighting)
function, and explicitly evaluate them for some specific spacetimes. In this
paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are
compact and without boundary. In the short "sampling time" limit, the bound has
asymptotic expansion. Although the expansion can not be represented by locally
invariant quantities in general due to the nonlocal nature of the integral, we
explicitly evaluate the dominant terms in the limit in terms of the invariant
quantities. We also make an estimate for the bound in the long sampling time
limit.Comment: LaTex, 23 Page
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