Finite State and Finite Stop Quantum Languages

We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition, the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq) and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. In this way, we establish two proper inclusion relations (fsqa) ⊂ (ftqa) and (icftq) ⊂ (vcftq), where the symbol means languages, and two infinite language hierarchies (fsqa) ⊂ (fsqa), (icftq) (icftq).     

A hybrid Finite Integration–Finite Volume Scheme

A hybridized scheme for the numerical solution of transient electromagnetic field problems is presented. The scheme combines the Finite Integration Technique (FIT) and the Finite Volume Method (FVM) in order to profit from the computational efficiency of the FIT while taking advantage of the superior dispersive properties of the FVM. The scheme is based on the longitudinal–transverse (LT) splitting of the discrete curl operator. The FIT is employed for discretizing the two-dimensional subproblem while the one-dimensional problem is discretized according to the FVM. The scheme offers benefits for the simulation of multiscale setups, where the size of the computational domain along one preferred direction is electrically much larger than along the others. In such situations, the accumulation of dispersion errors within hundreds of thousands of time steps usually deteriorates the solution accuracy. The hybrid scheme is applied in combination with adaptive mesh refinement, yielding an efficient scheme for multiscale applications.     

Finite Quantum Dynamics

We decontract the quantum harmonic oscillator dynamics to obtain a covariant finite quantum dynamics in quantum time. The usual central (“superselection”) time results from a condensation of events. Dynamics results from an entanglement of the oscillator quantum variables with the quantum time variable. Unitarity necessarily fails, slightly for middle times but grossly near the beginning and end of time. Time and energy interconvert during space-time meltdown, at a rate governed by a regulant like the Planck power.     

Finite ? Stellarators

A fully three-dimensional computer code based on an ideal magnetohydrodynamic model has been used to find stellarator configurations with finite critical values of the plasma parameter ?. It is established that the WISTOR-U torsatron designed at the University of Wisconsin and the Heliotron E experiment constructed at Kyoto University have average ? limits near 5 percent.     

Finite electromagnetic masses

A null-plane current commutator algebra, abstracted from a fermion theory, is shown to satisfy the Pagels condition for finite electromagnetic self-masses of hadrons.     

Finite Abnormal Nuclei

We solved the problem for both the normal and abnormal finite nuclei from a simple relativistic model,and found eritical mass numbers A₁=85 and A₂=165.Only nuclei with mass numbers A≥A₁ may bave bound abnormal states,and only abnormal nuclei with mass number A≥A₂ have binding energies larger than those of corresponding normal nuclei.Abnormal nuclei become unbound again if A>3310,because of the Coulomb repulsion.     

Finite supersymmetry transformations

We investigate simple examples of supersymmetry algebras with real and Grassmann parameters. Special attention is paid to the finite supertransformations and their probability interpretation. Furthermore we look for combinations of bosons and fermions which are invariant under supertransformations. These combinations correspond to states that are highly entangled.Received: 30 January 2004, Published online: 23 April 2004N. Ilieva: On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Boul. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria     

Finite unified models

We present phenomenologically viableSU (5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV.     

Finite volume Kolmogorov-Johnson-Mehl-Avrami theory

We study the Kolmogorov-Johnson-Mehl-Avrami theory of phase conversion in finite volumes. For the conversion time we find the relationship tau(con)=tau(nu)[1+f(d)(q)]. Here d is the space dimension, tau(nu) the nucleation time in the volume V, and f(d)(q) a scaling function. Its dimensionless argument is q=tau(ex)/tau(nu), where tau(ex) is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate f(d)(q) in one, two, and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for f(d)(q).     

Finite size Wilson loops

A study of Wilson loop averages for finite size loops is initiated. Within the framework of euclidean four-dimensional lattice SU(2) gauge theory with elementary Wilson action we compute the expectation values of all rectangular loops to 12th order in the strong coupling expansion. The leading term for weak coupling is evaluated for loops up to 4 × 4. A comparison to Monte Carlo data is presented. Other related issues are also discussed.     

Gravity on Finite Groups

Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S ₃ is treated in detail, and used to build a gravity-like field theory on S ₃. Received: 11 November 1999 / Accepted: 11 December 2000     

Finite size scale invariance

We develop a new approach to scale symmetry, which takes into account the possible finite cut-offs of the fields or the parameters. This new symmetry, called finite size scale symmetry: i) includes the traditional self-similarity as a limiting case, when the cut-offs are set to infinity (infinite size-system); ii) is consistent with the traditional finite size scaling approach already used in critical phenomena; iii) enables the computation of some of the universal functions appearing in the finite size scaling formulation; iv) allows scale transformations leaving the cut-offs invariant, like in the traditional renormalization approach; v) can be formulated to allow for positive or negative fields and parameters; vi) leads to new predictions about the shape of some distributions in critical phenomena or turbulence which are in very good agreement with the experimental or numerical findings. Received 26 January 1999 and Received in final form 25 October 1999     

Dirac Equation at Finite Temperature

In this paper, we propose finite temperature Dirac equation, which can describe the quantum systems in an arbitrary temperature for a relativistic particle of spin-1/2. When the temperature T=0, it become Dirac equation. With the equation, we can study the relativistic quantum systems in an arbitrary temperature.     

Quantum Measurements and Finite Geometry

A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric informationally complete positive-operator-valued measure, is, remarkably, also analogous to an affine plane, but with the roles of points and lines interchanged. In this paper I present these analogies and ask whether they shed any light on the existence or non-existence of such symmetric quantum measurements for a general quantum system with a finite-dimensional state space.     

Finite model of a crystal

A general expansion of the statistical sum is given for a finite model of a crystal. The multiplicative approximation, which leads to the Bazarov theory, is analyzed. The free energy of the crystal is evaluated.