15910786
Supersymmetric polytropic gas dynamics
Abstract We construct the N =1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of ‘‘ Eulerian" conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY-B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N =1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.
119417489
Generalized Benney lattice and the heavenly equation
We generalize the Benney lattice and show that the new system of equations can be reduced to a generalized Chaplygin gas as well as the heavenly equation. We construct two infinite sets of conserved charges and show that one of the sets can be obtained from the Lax function. The conserved densities are related to Legendre polynomials and we present closed form expressions for the generating functions for these densities which also determines the Riemann invariants of the problem. We prove that the system is bi-Hamiltonian and that the conserved charges are in involution with respect to either of the Hamiltonian structures. We show that the associated generalized elastic medium equations are bi-Hamiltonian as well. We also bring out various other interesting features of our model.
14154427
A NONSTANDARD SUPERSYMMETRIC KP HIERARCHY
We show that the supersymmetric nonlinear Schrodinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.
123461429
Supersymmetry and finite temperature
14374796
OUT OF EQUILIBRIUM PHASE TRANSITIONS AND A TOY MODEL FOR DISORIENTED CHIRAL CONDENSATES
We study the dynamics of a second order phase transition in a situation that mimics a sudden quench to a temperature below the critical temperature in a model with dynamical symmetry breaking. In particular we show that the domains of correlated values of the condensate grow as $\sqrt{t}$ and that this result seems to be largely model-independent.
119380448
DYNAMICAL SUPERSYMMETRY
We show, in a simple quantum mechanical model, how a theory can become supersymmetric in the presence of interactions even when the free theory is not. This dynamical generation of supersymmetry relaxes the condition on the equality of masses of the superpartners which would be of phenomenological interest.
17157423
A Lax description for polytropic gas dynamics
Abstract We give a Lax description for the system of polytropic gas equations. The special structure of the Lax function naturally leads to the two infinite sets of conserved charges associated with this system. We obtain closed form expressions for the conserved charges as well as the generating functions for them. We show how the study of these generating functions can naturally lead to the recursion relation between the conserved quantities as well as the higher-order Hamiltonian structures.