5,525 research outputs found
EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory
We discuss the problem of finding a Lorentz invariant extension of Bohmian
mechanics. Due to the nonlocality of the theory there is (for systems of more
than one particle) no obvious way to achieve such an extension. We present a
model invariant under a certain limit of Lorentz transformations, a limit
retaining the characteristic feature of relativity, the non-existence of
absolute time resp. simultaneity. The analysis of this model exemplifies an
important property of any Bohmian quantum theory: the quantum equilibrium
distribution cannot simultaneously be realized in all
Lorentz frames of reference.Comment: 24 pages, LaTex, 4 figure
A hydrodynamic approach to non-equilibrium conformal field theories
We develop a hydrodynamic approach to non-equilibrium conformal field theory.
We study non-equilibrium steady states in the context of one-dimensional
conformal field theory perturbed by the irrelevant operator. By
direct quantum computation, we show, to first order in the coupling, that a
relativistic hydrodynamic emerges, which is a simple modification of
one-dimensional conformal fluids. We show that it describes the steady state
and its approach, and we provide the main characteristics of the steady state,
which lies between two shock waves. The velocities of these shocks are modified
by the perturbation and equal the sound velocities of the asymptotic baths.
Pushing further this approach, we are led to conjecture that the approach to
the steady state is generically controlled by the power law , and
that the widths of the shocks increase with time according to .Comment: 24 page
How to project onto extended second order cones
The extended second order cones were introduced by S. Z. N\'emeth and G.
Zhang in [S. Z. N\'emeth and G. Zhang. Extended Lorentz cones and variational
inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for
solving mixed complementarity problems and variational inequalities on
cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended second
order cones. Journal of Global Optimization, 66(3):585-593, 2016] determined
the automorphism groups and the Lyapunov or bilinearity ranks of these cones.
S. Z. N\'emeth and G. Zhang in [S.Z. N\'emeth and G. Zhang. Positive operators
of Extended Lorentz cones. arXiv:1608.07455v2, 2016] found both necessary
conditions and sufficient conditions for a linear operator to be a positive
operator of an extended second order cone. This note will give formulas for
projecting onto the extended second order cones. In the most general case the
formula will depend on a piecewise linear equation for one real variable which
will be solved by using numerical methods
On hot bangs and the arrow of time in relativistic quantum field theory
A recently proposed method for the characterization and analysis of local
equilibrium states in relativistic quantum field theory is applied to a simple
model. Within this model states are identified which are locally (but not
globally) in thermal equilibrium and it is shown that their local thermal
properties evolve according to macroscopic equations. The largest space-time
regions in which local equilibrium states can exist are timelike cones. Thus,
although the model does not describe dissipative effects, such states fix in a
natural manner a time direction. Moreover, generically they determine a
distinguished space-time point where a singularity in the temperature (a hot
bang) must have occurred if local equilibrium prevailed thereafter. The results
illustrate how the breaking of the time reflection symmetry at macroscopic
scales manifests itself in a microscopic setting.Comment: 21 pages; v2: minor linguistic changes and some typos correcte
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