1,812 research outputs found
Information processing with Page-Wootters states
In order to perceive that a physical system evolves in time, two requirements
must be met: (a) it must be possible to define a "clock" and (b) it must be
possible to make a copy of the state of the system, that can be reliably
retrieved to make a comparison. We investigate what constraints quantum
mechanics poses on these issues, in light of recent experiments with entangled
photons.Comment: 9 pages LaTeX2e, 1 eps figure. Contribution to the special volume
"Chaos, Information Processing and Paradoxical Games", World Scientific
(2014
A particle in equilibrium with a bath realizes worldline supersymmetry
We study the relation between the partition function of a non--relativistic
particle, in one spatial dimension, that describes the equilibrium fluctuations
implicitly, and the partition function of the same system, deduced from the
Langevin equation, that describes the fluctuations explicitly, of a bath with
additive white--noise properties using Monte Carlo simulations for computing
the correlation functions that satisfy the corresponding identities. We show
that both can be related to the partition function of the corresponding,
maximally supersymmetric, theory with one--dimensional bosonic worldvolume, by
appropriate analytic continuation, from Euclidian to real time, and that they
can all describe the same physics, since the correlation functions of the
observables satisfy the same identities for all systems.The supersymmetric
theory provides the consistent closure for describing the fluctuations.
Therefore supersymmetry is relevant at the scale in which equilibrium with
the bath is meaningful. At scales when the "true" degrees of freedom of the
bath can be resolved (e.g. atoms and molecules for the case of thermal
fluctuations) the superpartners become "hidden". They can be, always, revealed
through the identities satisfied by the correlation functions of the
appropriate noise field, however.
In fact, the same formalism applies whatever the "microscopic" origin of the
fluctuations.
Therefore, all consistently closed physical systems are supersymmetric--and
any system that is explicitly not invariant under supersymmetric
transformations, is, in fact, open and, therefore, incomplete.Comment: 48 pages, many PNG figures, LaTeX2e. Requires utphys.bst for the
bibliography. v2: Extensively rewritten; errors corrected regarding the
"fermionic'' action and presentation clarified and sharpene
Layered Phase Investigations
The extra dimensional defects that are introduced to generate the lattice
chiral zero modes are not simply a computational trick, but have interesting
physical consequences. After reviewing what is known about the layered phase
they can generate, I argue how it is possible to simulate Yang-Mills theories
with reduced systematic errors and speculate on how it might be possible to
study the fluctuations of the layers' topological charge.Comment: 5 pages (LaTeX, PoS class file included); Contribution to the XXV
International Symposium on Lattice Field Theory,July 30 - August 4
2007,Regensburg, German
Galilean currents and charges
We derive the Noether currents and charges associated with an internal
galilean invariance---a symmetry recently postulated in the context of
so-called galileon theories. Along the way we clarify the physical
interpretation of the Noether charges associated with ordinary Galileo- and
Lorentz-boosts.Comment: 5 page
Supersymmetric probability distributions
We use anticommuting variables to study probability distributions of random
variables, that are solutions of Langevin's equation. We show that the
probability density always enjoys "worldpoint supersymmetry". The partition
function, however, may not. We find that the domain of integration can acquire
a boundary, that implies that the auxiliary field has a non-zero expectation
value, signalling spontaneous supersymmetry breaking. This is due to the
presence of "fermionic" zeromodes, whose contribution cannot be cancelled by a
surface term. This we prove by an explicit calculation of the regularized
partition function, as well as by computing the moments of the auxiliary field
and checking whether they satisfy the identities implied by Wick's theorem.
Nevertheless, supersymmetry manifests itself in the identities that are
satisfied by the moments of the scalar, whose expressions we can calculate,for
all values of the coupling constant. We also provide some quantitative
estimates concerning the visibility of supersymmetry breaking effects in the
identities for the moments and remark that the shape of the distribution of the
auxiliary field can influence quite strongly how easy it would be to mask them,
since the expectation value of the auxiliary field doesn't coincide with its
typical value.Comment: LaTeX2e: 24 pages, 7 figure
Unitary Evolution on a Discrete Phase Space
We construct unitary evolution operators on a phase space with power of two
discretization. These operators realize the metaplectic representation of the
modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the
non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative
field theories as well as theories of quantum space-time. The class of
operators may also be useful for the efficient realization of new quantum
algorithms.Comment: 5 pages, contribution to Lattice 2005 (theoretical developments
Knotted Strange Attractors and Matrix Lorenz Systems
A generalization of the Lorenz equations is proposed where the variables take
values in a Lie algebra. The finite dimensionality of the representation
encodes the quantum fluctuations, while the non-linear nature of the equations
can describe chaotic fluctuations. We identify a criterion, for the appearance
of such non-linear terms. This depends on whether an invariant, symmetric
tensor of the algebra can vanish or not. This proposal is studied in detail for
the fundamental representation of . We find a knotted
structure for the attractor, a bimodal distribution for the largest Lyapunov
exponent and that the dynamics takes place within the Cartan subalgebra, that
does not contain only the identity matrix, thereby can describe the quantum
fluctuations.Comment: 10 pages Revtex, 3 figure
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