1,982 research outputs found
Nonlinear equations for p-adic open, closed, and open-closed strings
We investigate the structure of solutions of boundary value problems for a
one-dimensional nonlinear system of pseudodifferential equations describing the
dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar
tachyon field using the method of successive approximations. For an open-closed
string, we prove that the method converges for odd values of p of the form
p=4n+1 under the condition that the solution for the closed string is known.
For p=2, we discuss the questions of the existence and the nonexistence of
solutions of boundary value problems and indicate the possibility of
discontinuous solutions appearing.Comment: 16 pages, 3 figure
Nonlocal Dynamics of p-Adic Strings
We consider the construction of Lagrangians that might be suitable for
describing the entire -adic sector of an adelic open scalar string. These
Lagrangians are constructed using the Lagrangian for -adic strings with an
arbitrary prime number . They contain space-time nonlocality because of the
d'Alembertian in argument of the Riemann zeta function. We present a brief
review and some new results.Comment: 8 page
Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold
We derive non-linear recursion equation for the leading infrared logarithms
(LL) in four dimensional sigma-model with fields on an arbitrary Riemann
manifold. The derived equation allows one to compute leading infrared
logarithms to essentially unlimited loop order in terms of geometric
characteristics of the Riemann manifold.
We reduce the solution of the SU(oo) principal chiral field in arbitrary
number of dimensions in the LL approximation to the solution of very simple
recursive equation. This result paves a way to the solution of the model in
arbitrary number of dimensions at N-->ooComment: Talk given by MVP at the conference devoted to memory of A.N.
Vasilie
Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups
The quantum group G_r,s provides a realisation of the two parameter quantum
GL_p,q(2) which is known to be related to the two parameter nonstandard
GL_hh'(2) group via a contraction method. We apply the contraction procedure to
G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a
realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then
extended to the coloured quantum group GL_r{\lambda,\mu}(2) to yield a new
Jordanian quantum group GL_m{\lambda,\mu}(2). Both G_r,s and G_m,k are then
generalised to their coloured versions which inturn provide similar
realisations of GL_r{\lambda,\mu}(2) and GL_m{\lambda,\mu}(2).Comment: 22 pages LaTeX, to be published in J. Math. Phy
Instability of ion kinetic waves in a weakly ionized plasma
The fundamental higher-order Landau plasma modes are known to be generally
heavily damped. We show that these modes for the ion component in a weakly
ionized plasma can be substantially modified by ion-neutral collisions and a dc
electric field driving ion flow so that some of them can become unstable. This
instability is expected to naturally occur in presheaths of gas discharges at
sufficiently small pressures and thus affect sheaths and discharge structures.Comment: Published in Phys. Rev. E, see
http://link.aps.org/doi/10.1103/PhysRevE.85.02641
p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency
The classical and quantum formalism for a p-adic and adelic harmonic
oscillator with time-dependent frequency is developed, and general formulae for
main theoretical quantities are obtained. In particular, the p-adic propagator
is calculated, and the existence of a simple vacuum state as well as adelic
quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical
phase are noted.Comment: 10 page
Opto-Acoustic Method of Tissue Oxygenation and its Biomedical Application
Novel opto-acoustic method of tissue oxygenation and restoring normal cell metabolism is proposed. The results of in vivo investigation the phenomenon of laser-induced photodissociation of blood oxyhemoglobin and its biomedical applications are presented. Photodissociation of oxyhemoglobin, the main biological function of which is oxygen transportation gives a unique possibility of additional oxygen extraction for restoring normal cell metabolism. Optical method of determination the therapeutic “dose” based on the response of changes in tissue oxygen concentration in dependence on wavelength and intensity of laser radiation has been developed. It is shown that in order to make the methods of phototherapy as well as laser therapy really efficient one has to control the oxygen concentration in tissue keeping it at the necessary level
Critical exponents from parallel plate geometries subject to periodic and antiperiodic boundary conditions
We introduce a renormalized 1PI vertex part scalar field theory setting in
momentum space to computing the critical exponents and , at least
at two-loop order, for a layered parallel plate geometry separated by a
distance L, with periodic as well as antiperiodic boundary conditions on the
plates. We utilize massive and massless fields in order to extract the
exponents in independent ultraviolet and infrared scaling analysis,
respectively, which are required in a complete description of the scaling
regions for finite size systems. We prove that fixed points and other critical
amounts either in the ultraviolet or in the infrared regime dependent on the
plates boundary condition are a general feature of normalization conditions. We
introduce a new description of typical crossover regimes occurring in finite
size systems. Avoiding these crossovers, the three regions of finite size
scaling present for each of these boundary conditions are shown to be
indistinguishable in the results of the exponents in periodic and antiperiodic
conditions, which coincide with those from the (bulk) infinite system.Comment: Modified introduction and some references; new crossover regimes
discussion improved; Appendixes expanded. 48 pages, no figure
Nonlinear dynamics of large amplitude dust acoustic shocks and solitary pulses in dusty plasmas
We present a fully nonlinear theory for dust acoustic (DA) shocks and DA
solitary pulses in a strongly coupled dusty plasma, which have been recently
observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002
(2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay
et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a
generalized hydrodynamic model for the strongly coupled dust grains, accounting
for arbitrary large amplitude dust number density compressions and potential
distributions associated with fully nonlinear nonstationary DA waves.
Time-dependent numerical solutions of our nonlinear model compare favorably
well with the recent experimental works (mentioned above) that have reported
the formation of large amplitude non-stationary DA shocks and DA solitary
pulses in low-temperature dusty plasma discharges.Comment: 9 pages, 4 figures. To be published in Physical Review
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
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