2,470 research outputs found
Semiclassical Expansions, the Strong Quantum Limit, and Duality
We show how to complement Feynman's exponential of the action so that it
exhibits a Z_2 duality symmetry. The latter illustrates a relativity principle
for the notion of quantum versus classical.Comment: 5 pages, references adde
A Quantum-Gravity Perspective on Semiclassical vs. Strong-Quantum Duality
It has been argued that, underlying M-theoretic dualities, there should exist
a symmetry relating the semiclassical and the strong-quantum regimes of a given
action integral. On the other hand, a field-theoretic exchange between long and
short distances (similar in nature to the T-duality of strings) has been shown
to provide a starting point for quantum gravity, in that this exchange enforces
the existence of a fundamental length scale on spacetime. In this letter we
prove that the above semiclassical vs. strong-quantum symmetry is equivalent to
the exchange of long and short distances. Hence the former symmetry, as much as
the latter, also enforces the existence of a length scale. We apply these facts
in order to classify all possible duality groups of a given action integral on
spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page
Skyrmion on a three--cylinder
The class of static, spherically symmetric, and finite energy hedgehog
solutions in the SU(2) Skyrme model is examined on a metric three-cylinder. The
exact analytic shape function of the 1-Skyrmion is found. It can be expressed
via elliptic integrals. Its energy is calculated, and its stability with
respect to radial and spherically symmetric deformations is analyzed. No other
topologically nontrivial solutions belonging to this class are possible on the
three-cylinder.Comment: v2: version accepted for publication in Phys. Rev.
Can one count the shape of a drum?
Sequences of nodal counts store information on the geometry (metric) of the
domain where the wave equation is considered. To demonstrate this statement, we
consider the eigenfunctions of the Laplace-Beltrami operator on surfaces of
revolution. Arranging the wave functions by increasing values of the
eigenvalues, and counting the number of their nodal domains, we obtain the
nodal sequence whose properties we study. This sequence is expressed as a trace
formula, which consists of a smooth (Weyl-like) part which depends on global
geometrical parameters, and a fluctuating part which involves the classical
periodic orbits on the torus and their actions (lengths). The geometrical
content of the nodal sequence is thus explicitly revealed.Comment: 4 pages, 1 figur
Invariant Regions and Global Asymptotic Stability in an Isothermal Catalyst
A well-known model for the evolution of the (space-dependent) concentration and (lumped) temperature in a porous catalyst is considered. A sequence of invariant regions of the phase space is given, which converges to a globally asymptotically stable region . Quantitative sufficient conditions are obtained for (the region to consist of only one point and) the problem to have a (unique) globally asymptotically stable steady state
Generalization of Einstein-Lovelock theory to higher order dilaton gravity
A higher order theory of dilaton gravity is constructed as a generalization
of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms
with higher powers of the Riemann tensor and of the first two derivatives of
the dilaton. Nevertheless, the resulting equations of motion are quasi-linear
in the second derivatives of the metric and of the dilaton. This property is
crucial for the existence of brane solutions in the thin wall limit. At each
order in derivatives the contribution to the Lagrangian is unique up to an
overall normalization. Relations between symmetries of this theory and the
O(d,d) symmetry of the string-inspired models are discussed.Comment: 18 pages, references added, version to be publishe
Distortions Of The Phase Space Behavior Of A Particle During one-third integral Resonance Extraction
Nodal domains on quantum graphs
We consider the real eigenfunctions of the Schr\"odinger operator on graphs,
and count their nodal domains. The number of nodal domains fluctuates within an
interval whose size equals the number of bonds . For well connected graphs,
with incommensurate bond lengths, the distribution of the number of nodal
domains in the interval mentioned above approaches a Gaussian distribution in
the limit when the number of vertices is large. The approach to this limit is
not simple, and we discuss it in detail. At the same time we define a random
wave model for graphs, and compare the predictions of this model with analytic
and numerical computations.Comment: 19 pages, uses IOP journal style file
High orders of Weyl series for the heat content
This article concerns the Weyl series of spectral functions associated with
the Dirichlet Laplacian in a -dimensional domain with a smooth boundary. In
the case of the heat kernel, Berry and Howls predicted the asymptotic form of
the Weyl series characterized by a set of parameters. Here, we concentrate on
another spectral function, the (normalized) heat content. We show on several
exactly solvable examples that, for even , the same asymptotic formula is
valid with different values of the parameters. The considered domains are
-dimensional balls and two limiting cases of the elliptic domain with
eccentricity : A slightly deformed disk () and an
extremely prolonged ellipse (). These cases include 2D domains
with circular symmetry and those with only one shortest periodic orbit for the
classical billiard. We analyse also the heat content for the balls in odd
dimensions for which the asymptotic form of the Weyl series changes
significantly.Comment: 20 pages, 1 figur
Effective capillary interaction of spherical particles at fluid interfaces
We present a detailed analysis of the effective force between two smooth
spherical colloids floating at a fluid interface due to deformations of the
interface. The results hold in general and are applicable independently of the
source of the deformation provided the capillary deformations are small so that
a superposition approximation for the deformations is valid. We conclude that
an effective long--ranged attraction is possible if the net force on the system
does not vanish. Otherwise, the interaction is short--ranged and cannot be
computed reliably based on the superposition approximation. As an application,
we consider the case of like--charged, smooth nanoparticles and
electrostatically induced capillary deformation. The resulting long--ranged
capillary attraction can be easily tuned by a relatively small external
electrostatic field, but it cannot explain recent experimental observations of
attraction if these experimental systems were indeed isolated.Comment: 23 page
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