We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution
U. We require that this global evolution
U be ...unitary, in accordance with quantum theory, and that this global evolution
U be causal, in accordance with special relativity. By causal we mean that information can only ever be transmitted at a bounded speed, the speed bound being quite naturally that of one edge of the underlying graph per iteration of
U. We show that under these conditions the operator
U can be implemented locally; i.e. it can be put into the form of a quantum circuit made up with more elementary operators — each acting solely upon neighboring nodes. We take quantum cellular automata as an example application of this representation theorem: this analysis bridges the gap between the axiomatic and the constructive approaches to defining QCA.
We realize Lobachevsky geometry in a simulation lab, by producing a carbon-based energetically stable molecular structure, arranged in the shape of a Beltrami pseudosphere. We find that this ...structure: (i) corresponds to a non-Euclidean crystallographic group, namely a loxodromic subgroup of ; (ii) has an unavoidable singular boundary, that we fully take into account. Our approach, substantiated by extensive numerical simulations of Beltrami pseudospheres of different size, might be applied to other surfaces of constant negative Gaussian curvature, and points to a general procedure to generate them. Our results also pave the way to test certain scenarios of the physics of curved spacetimes owing to graphene's unique properties.
The emergence of a minimal observable length of order of the Planck scale is a prediction of many quantum theories of gravity. However, the question arises as to whether this is a real fundamental ...length affecting nature in all of its facets, including spacetime. In this work, we show that the quantum measurement process implies the existence of a minimal measurable length and consequently the apparent discretization of spacetime. The obtained result is used to infer the value of zero-point energy in the universe, which is found to be in good agreement with the observed cosmological constant. This potentially offers some hints towards the resolution of the cosmological constant problem.
We use a top-down approach to explain physics of consciousness. We first focuse on the universe and propose a model discretization of the universe based on a T3-torus. An attempt is made to relate ...natural Planck units to the parameters of elementary geometric cells. We mention a way of approaching the horizon problem in discrete contest, as well. A suggestion for the discretization of the matter lagrangian part is also given. Then, by introducing a many-body method, we speculate on the binding energy in the very early universe and attempt to explain the source of a kind of dark energy that caused the inflation period. Finally, we focuse on the mind as a subset of the universe which is embeded in it and attempt to explain the source of consciousness as the "mind energy".
One considers the discrete space-time geometry
G
d
, which is given on the set of points (events), where the geometry of Minkowski is given. This discrete geometry is not a geometry on lattice. ...Motion of a free particle is considered in
G
d
. Free motion in
G
d
can be reduced to a motion in geometry of Minkowski
G
M
in some force field. Primordial free motion in
G
d
appears to be stochastic. In
G
M
it is difficult to describe the force field responsible for stochastic motion of a particle. The nature of this force field appears to be geometrical.
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described ...completely by the world function. The discrete geometry is nonaxiomatizable and multivariant. The equivalence relation is intransitive in the discrete geometry. The particles are described by world chains (broken lines with finite length of links), because in the discrete space-time geometry there are no infinitesimal lengths. Motion of particles is stochastic, and statistical description of them leads to the Schrödinger equation, if the elementary length of the discrete geometry depends on the quantum constant in a proper way.
Our theory of the origins of the universe based on old inflationary theory makes the minimum of assumptions, yet is consistent with observations. The properties of the scalar field, the discrete ...nonsymmetric phase, and their interactions are examined. Immediate consequences are that regions of the new phase never merge but persist as islands in the scalar field, and that the persistent scalar field is responsible for the effects attributed to cold dark matter. c 2010 Physics Essays Publication. DOI: 10.4006/1.3425751
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for ...discrete space-time.
The introduction of a discrete space-time represents an attempt to describe the physics at the Planck's scale. We show that this concept can be also very useful in describing thermodynamics in a ...pre-relativistic world. From this concept a new approach of statistical mechanics based on a dynamic viewpoint and an entropy representation is presented. The entropy is connected with the counting of the paths in space-time. It contains a time interval that represents the time that we have to wait in order to relax the quantum fluctuations and to reach the thermal regime. It is shown that this time is β hbar. The mathematical expressions we derive for thermal quantities like the entropy and the free energy are identical to those obtained by the traditional path-integral formalism starting from the canonical form of the thermal density matrix. However, the introduction of a quantized space-time shows that thermodynamics is consistent with an equation of motion that is time-irreversible at a microscopic level. As a consequence, the problem of irreversibility is revisited and the derivation of a H-theorem becomes possible in the future.
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