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 $\mathfrak{u}(2)$. 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