46,850 research outputs found
Semiclassical Trace Formulas for Noninteracting Identical Particles
We extend the Gutzwiller trace formula to systems of noninteracting identical
particles. The standard relation for isolated orbits does not apply since the
energy of each particle is separately conserved causing the periodic orbits to
occur in continuous families. The identical nature of the particles also
introduces discrete permutational symmetries. We exploit the formalism of
Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied
semiclassical dynamics in the presence of continuous symmetries, to derive
many-body trace formulas for the full and symmetry-reduced densities of states.
Numerical studies of the three-particle cardioid billiard are used to
explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR
Joint probability distributions and fluctuation theorems
We derive various exact results for Markovian systems that spontaneously
relax to a non-equilibrium steady-state by using joint probability
distributions symmetries of different entropy production decompositions. The
analytical approach is applied to diverse problems such as the description of
the fluctuations induced by experimental errors, for unveiling symmetries of
correlation functions appearing in fluctuation-dissipation relations recently
generalised to non-equilibrium steady-states, and also for mapping averages
between different trajectory-based dynamical ensembles. Many known fluctuation
theorems arise as special instances of our approach, for particular two-fold
decompositions of the total entropy production. As a complement, we also
briefly review and synthesise the variety of fluctuation theorems applying to
stochastic dynamics of both, continuous systems described by a Langevin
dynamics and discrete systems obeying a Markov dynamics, emphasising how these
results emerge from distinct symmetries of the dynamical entropy of the
trajectory followed by the system For Langevin dynamics, we embed the "dual
dynamics" with a physical meaning, and for Markov systems we show how the
fluctuation theorems translate into symmetries of modified evolution operators.Comment: 39 pages, 1 figure. Minor revision, as suggested by referees. A
couple of references and equations added. Acknowledgements slightly modifie
Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics.
A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermo dynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method
On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
The continuous and discrete symmetries of the Kuramoto-Sivashinsky system
restricted to a spatially periodic domain play a prominent role in shaping the
invariant sets of its chaotic dynamics. The continuous spatial translation
symmetry leads to relative equilibrium (traveling wave) and relative periodic
orbit (modulated traveling wave) solutions. The discrete symmetries lead to
existence of equilibrium and periodic orbit solutions, induce decomposition of
state space into invariant subspaces, and enforce certain structurally stable
heteroclinic connections between equilibria. We show, on the example of a
particular small-cell Kuramoto-Sivashinsky system, how the geometry of its
dynamical state space is organized by a rigid `cage' built by heteroclinic
connections between equilibria, and demonstrate the preponderance of unstable
relative periodic orbits and their likely role as the skeleton underpinning
spatiotemporal turbulence in systems with continuous symmetries. We also offer
novel visualizations of the high-dimensional Kuramoto-Sivashinsky state space
flow through projections onto low-dimensional, PDE representation independent,
dynamically invariant intrinsic coordinate frames, as well as in terms of the
physical, symmetry invariant energy transfer rates.Comment: 31 pages, 17 figures; added references, corrected typos. Due to file
size restrictions some figures in this preprint are of low quality. A high
quality copy may be obtained from
http://www.cns.gatech.edu/~predrag/papers/preprints.html#rp
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