218 research outputs found
Invariance in adelic quantum mechanics
Adelic quantum mechanics is form invariant under an interchange of real and
p-adic number fields as well as rings of p-adic integers. We also show that in
adelic quantum mechanics Feynman's path integrals for quadratic actions with
rational coefficients are invariant under changes of their entries within
nonzero rational numbers.Comment: 6 page
Airy functions over local fields
Airy integrals are very classical but in recent years they have been
generalized to higher dimensions and these generalizations have proved to be
very useful in studying the topology of the moduli spaces of curves. We study a
natural generalization of these integrals when the ground field is a
non-archimedean local field such as the field of p-adic numbers. We prove that
the p-adic Airy integrals are locally constant functions of moderate growth and
present evidence that the Airy integrals associated to compact p-adic Lie
groups also have these properties.Comment: Minor change
Randomness in Classical Mechanics and Quantum Mechanics
The Copenhagen interpretation of quantum mechanics assumes the existence of
the classical deterministic Newtonian world. We argue that in fact the Newton
determinism in classical world does not hold and in classical mechanics there
is fundamental and irreducible randomness. The classical Newtonian trajectory
does not have a direct physical meaning since arbitrary real numbers are not
observable. There are classical uncertainty relations, i.e. the uncertainty
(errors of observation) in the determination of coordinate and momentum is
always positive (non zero).
A "functional" formulation of classical mechanics was suggested. The
fundamental equation of the microscopic dynamics in the functional approach is
not the Newton equation but the Liouville equation for the distribution
function of the single particle. Solutions of the Liouville equation have the
property of delocalization which accounts for irreversibility. The Newton
equation in this approach appears as an approximate equation describing the
dynamics of the average values of the position and momenta for not too long
time intervals. Corrections to the Newton trajectories are computed. An
interpretation of quantum mechanics is attempted in which both classical and
quantum mechanics contain fundamental randomness. Instead of an ensemble of
events one introduces an ensemble of observers.Comment: 12 pages, Late
On a initial value problem arising in mechanics
We study initial value problem for a system consisting of an integer order
and distributed-order fractional differential equation describing forced
oscillations of a body attached to a free end of a light viscoelastic rod.
Explicit form of a solution for a class of linear viscoelastic solids is given
in terms of a convolution integral. Restrictions on storage and loss moduli
following from the Second Law of Thermodynamics play the crucial role in
establishing the form of the solution. Some previous results are shown to be
special cases of the present analysis
Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
We derive equations of motion for the tachyon field living on an unstable
non-BPS D-brane in the level truncated open cubic superstring field theory in
the first non-trivial approximation. We construct a special time dependent
solution to this equation which describes the rolling tachyon. It starts from
the perturbative vacuum and approaches one of stable vacua in infinite time. We
investigate conserved energy functional and show that its different parts
dominate in different stages of the evolution. We show that the pressure for
this solution has its minimum at zero time and goes to minus energy at infinite
time.Comment: 16 pages, 5 figures; minor correction
Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation
A generalized approach to the quantization of a large class of maps on a
torus, i.e. quantization via the von Neumann Equation, is described and a
number of issues related to the quantization of model systems are discussed.
The approach yields well behaved mixed quantum states for tori for which the
corresponding Schrodinger equation has no solutions, as well as an extended
spectrum for tori where the Schrodinger equation can be solved.
Quantum-classical correspondence is demonstrated for the class of mappings
considered, with the Wigner-Weyl density going to the correct
classical limit. An application to the cat map yields, in a direct manner,
nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the
correspondence limit.Comment: 36 pages, RevTex preprint forma
Soft and hard wall in a stochastic reaction diffusion equation
We consider a stochastically perturbed reaction diffusion equation in a
bounded interval, with boundary conditions imposing the two stable phases at
the endpoints. We investigate the asymptotic behavior of the front separating
the two stable phases, as the intensity of the noise vanishes and the size of
the interval diverges. In particular, we prove that, in a suitable scaling
limit, the front evolves according to a one-dimensional diffusion process with
a non-linear drift accounting for a "soft" repulsion from the boundary. We
finally show how a "hard" repulsion can be obtained by an extra diffusive
scaling.Comment: 33 page
Supersymmetric null-surfaces
Single trace operators with the large R-charge in supersymmetric Yang-Mills
theory correspond to the null-surfaces in . We argue that the
moduli space of the null-surfaces is the space of contours in the
super-Grassmanian parametrizing the complex -dimensional subspaces of
the complex -dimensional space. The odd coordinates on this
super-Grassmanian correspond to the fermionic degrees of freedom of the
superstring.Comment: v4: added a reference to the earlier work; corrected the formula for
the stabilizer of the BMN vacuum; added the discussion of the complex
structure of the odd coordinates in Section 3.
Bouncing and Accelerating Solutions in Nonlocal Stringy Models
A general class of cosmological models driven by a non-local scalar field
inspired by string field theories is studied. In particular cases the scalar
field is a string dilaton or a string tachyon. A distinguished feature of these
models is a crossing of the phantom divide. We reveal the nature of this
phenomena showing that it is caused by an equivalence of the initial non-local
model to a model with an infinite number of local fields some of which are
ghosts. Deformations of the model that admit exact solutions are constructed.
These deformations contain locking potentials that stabilize solutions.
Bouncing and accelerating solutions are presented.Comment: Minor corrections, references added, published in JHE
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