2,877 research outputs found
The Marriage Problem and the Fate of Bachelors
In the marriage problem, a variant of the bi-parted matching problem, each
member has a `wish-list' expressing his/her preference for all possible
partners; this list consists of random, positive real numbers drawn from a
certain distribution. One searches the lowest cost for the society, at the risk
of breaking up pairs in the course of time. Minimization of a global cost
function (Hamiltonian) is performed with statistical mechanics techniques at a
finite fictitious temperature.
The problem is generalized to include bachelors, needed in particular when
the groups have different size, and polygamy. Exact solutions are found for the
optimal solution (T=0). The entropy is found to vanish quadratically in .
Also other evidence is found that the replica symmetric solution is exact,
implying at most a polynomial degeneracy of the optimal solution.
Whether bachelors occur or not, depends not only on their intrinsic
qualities, or lack thereof, but also on global aspects of the chance for pair
formation in society.Comment: 14 pages revtex, submitted to Physica
Thermodynamic picture of the glassy state gained from exactly solvable models
A picture for thermodynamics of the glassy state was introduced recently by
us (Phys. Rev. Lett. {\bf 79} (1997) 1317; {\bf 80} (1998) 5580). It starts by
assuming that one extra parameter, the effective temperature, is needed to
describe the glassy state. This approach connects responses of macroscopic
observables to a field change with their temporal fluctuations, and with the
fluctuation-dissipation relation, in a generalized, non-equilibrium way.
Similar universal relations do not hold between energy fluctuations and the
specific heat.
In the present paper the underlying arguments are discussed in greater
length. The main part of the paper involves details of the exact dynamical
solution of two simple models introduced recently: uncoupled harmonic
oscillators subject to parallel Monte Carlo dynamics, and independent spherical
spins in a random field with such dynamics. At low temperature the relaxation
time of both models diverges as an Arrhenius law, which causes glassy behavior
in typical situations. In the glassy regime we are able to verify the above
mentioned relations for the thermodynamics of the glassy state.
In the course of the analysis it is argued that stretched exponential
behavior is not a fundamental property of the glassy state, though it may be
useful for fitting in a limited parameter regime.Comment: revised version, 38 pages, 9 figure
Thermodynamics of the glassy state
A picture for thermodynamics of the glassy state is introduced. It assumes
that one extra parameter, the effective temperature, is needed to describe the
glassy state. This explains the classical paradoxes concerning the Ehrenfest
relations and the Prigogine-Defay ratio. As a second part, the approach
connects the response of macroscopic observables to a field change with their
temporal fluctuations, and with the fluctuation-dissipation relation, in a
generalized non-equilibrium way.Comment: 12 pages, including 2 figures. To appear in: 8th Tohwa University
Int'l Symposium on Slow Dynamics in Complex System
Classical Phase Space Density for the Relativistic Hydrogen Atom
Quantum mechanics is considered to arise from an underlying classical
structure (``hidden variable theory'', ``sub-quantum mechanics''), where
quantum fluctuations follow from a physical noise mechanism. The stability of
the hydrogen ground state can then arise from a balance between Lorentz damping
and energy absorption from the noise. Since the damping is weak, the ground
state phase space density should predominantly be a function of the conserved
quantities, energy and angular momentum.
A candidate for this phase space density is constructed for ground state of
the relativistic hydrogen problem of a spinless particle. The first excited
states and their spherical harmonics are also considered in this framework. The
analytic expression of the ground state energy can be reproduced, provided
averages of certain products are replaced by products of averages. This
analysis puts forward that quantum mechanics may arise from an underlying
classical level as a slow variable theory, where each new quantum operator
relates to a new, well separated time interval.Comment: 15pages AIP tex with 1 Figur
A puzzle on fluctuations of weights in spin glasses
In certain mean field models for spin glasses there occurs a one step replica
symmetry breaking pattern. As an example of general -corrections in such
systems, the fluctuations in the internal energy are calculated. For this
specific quantity the outcome is known from the specific heat. It is shown that
the correct result can be derived by assuming that the both the height and the
location of the breakpoint fluctuate. This effect enlarges the commonly
considered space of allowed fluctuations of the order parameter in loop
calculations for short range spin glasses of this type. The phenomenon does not
occur in spin glasses with infinite order replica symmetry breaking.Comment: 7 pages RevTex Revised version, to appear in: Journal de Physique
(January 96
Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
The Schwarzschild-de Sitter and Reissner-Nordstr\"om-de Sitter black hole
metrics appear as exact solutions in the recently formulated massive gravity of
de Rham, Gabadadze and Tolley (dRGT), where the mass term sets the curvature
scale. They occur within a two-parameter family of dGRT mass terms. They show
no trace of a cloud of scalar graviton modes, and in the limit of vanishing
graviton mass they go smoothly to the Schwarzschild and Reissner-Nordstr\"om
metrics.Comment: 4 page
On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics
de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen
problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003
simulations support the stability, our recent numerics always lead to
self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic
orbits. For very eccentric orbits with energy close to zero and angular
momentum below some not-small value, there is on the average a net gain in
energy for each revolution, which explains the self-ionisation. Next, an
potential is added, which could stem from a dipolar deformation of the
nuclear charge by the electron at its moving position. This shape retains the
analytical solvability. When it is enough repulsive, the ground state of this
modified hydrogen problem is predicted to be stable. The same conclusions hold
for positronium.Comment: 18 pages latex, 1 figur
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