Search results for "Quantum"

showing 10 items of 9714 documents

On the exponential growth of graded Capelli polynomials

2013

In a free superalgebra over a field of characteristic zero we consider the graded Capelli polynomials Cap M+1[Y,X] and Cap L+1[Z,X] alternating on M+1 even variables and L+1 odd variables, respectively. Here we compute the superexponent of the variety of superalgebras determinated by Cap M+1[Y,X] and Cap L+1[Z,X]. An essential tool in our computation is the generalized-six-square theorem proved in [3].

CombinatoricsSettore MAT/02 - AlgebraExponential growthMathematics::Quantum AlgebraGeneral MathematicsZero (complex analysis)algebras with pilynomial identities noncommutative invariant theory asymptotic equivalenceField (mathematics)Algebra over a fieldVariety (universal algebra)Mathematics::Representation TheorySuperalgebraMathematicsIsrael Journal of Mathematics
researchProduct

Quantum Identification of Boolean Oracles

2004

The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \…

CombinatoricsStatistics::TheoryLog-log plotTheoryofComputation_GENERALQuantum walkQuantum algorithmComputer Science::Computational ComplexityBoolean functionUpper and lower boundsOracleQuantum computerMathematicsRandom oracle
researchProduct

Entropy, transverse entropy and partitions of unity

1994

AbstractThe topological entropy of a transformation is expressed in terms of partitions of unity. The transverse entropy of a flow tangential to a foliation is defined and expresed in a similar way. The geometric entropy of a foliation of a Riemannian manifold is compared with the transverse entropy of its geodesic flow.

CombinatoricsTransverse planeEntropy (classical thermodynamics)Applied MathematicsGeneral MathematicsConfiguration entropyMaximum entropy probability distributionMathematics::Differential GeometryStatistical physicsJoint quantum entropyMathematicsErgodic Theory and Dynamical Systems
researchProduct

Pizza-cutter’s problem and Hamiltonian paths

2019

Summary. The pizza-cutter’s problem is to determine the maximum number of pieces that can be made with n straight cuts through a circular pizza, regardless of the size and shape of the pieces. For ...

Combinatoricssymbols.namesakeGeneral Mathematics010102 general mathematics[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]symbols0101 mathematicsHamiltonian (quantum mechanics)01 natural sciencesComputingMilieux_MISCELLANEOUSMathematics
researchProduct

Commutator anomalies and the Fock bundle

1990

We show that the anomalous finite gauge transformations can be realized as linear operators acting on sections of the bundle of fermionic Fock spaces parametrized by vector potentials, and more generally, by splittings of the fermionic one-particle space into a pair of complementary subspaces. On the Lie algebra level we show that the construction leads to the standard formula for the relevant commutator anomalies.

CommutatorHigh Energy Physics::Lattice58D30Statistical and Nonlinear Physics58B25Space (mathematics)Linear subspace58G35Fock spaceLinear map81D07Quantum mechanicsLie algebraGauge theoryAnomaly (physics)Mathematical PhysicsMathematical physicsMathematics81E13
researchProduct

Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality

2018

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …

Compatible and incompatible questionPsychology (all)Uncertainty principleInequalityComputer sciencemedia_common.quotation_subjectMental stateHeisenberg uncertainty principle050105 experimental psychology03 medical and health sciencessymbols.namesake0302 clinical medicine0501 psychology and cognitive sciencesQuantumGeneral Psychologymedia_commonApplied Mathematics05 social sciencesHilbert spaceObservableDecision problemOrder effect16. Peace & justiceHermitian matrixMental statesymbolsDecision makingMathematical economics030217 neurology & neurosurgery
researchProduct

An example of cancellation of infinities in the star-quantization of fields

1993

Within the *-quantization framework, it is shown how to remove some of the divergences occurring in theλo 2 4 -theory by introducing aλ-dependent *-product cohomologically equivalent to the normal *-product.

Complex systemStatistical and Nonlinear PhysicsTopologyRenormalizationsymbols.namesakeTheoretical physicsSingularityHamiltonian formalismRegularization (physics)symbolsQuantum field theoryHamiltonian (quantum mechanics)Mathematical PhysicsMathematicsLetters in Mathematical Physics
researchProduct

Codification schemes and finite automata

2000

This paper is a note on how Information Theory and Codification Theory are helpful in the computational design both of communication protocols and strategy sets in the framework of finitely repeated games played by boundedly rational agents. More precisely, we show the usefulness of both theories to improve the existing automata bounds of Neyman¿s (1998) work on finitely repeated games played by finite automata.

Complexity codification repeated games finite automataTheoretical computer scienceFinite-state machineSociology and Political Sciencejel:C72jel:C73ComputingMilieux_PERSONALCOMPUTINGGeneral Social SciencesRational agentInformation theoryAutomatonRepeated gameAutomata theoryQuantum finite automataStatistics Probability and UncertaintyCommunications protocolGeneral PsychologyMathematicsMathematical Social Sciences
researchProduct

Appearances of pseudo-bosons from Black-Scholes equation

2016

It is a well known fact that the Black-Scholes equation admits an alternative representation as a Schr\"odinger equation expressed in terms of a non self-adjoint hamiltonian. We show how {\em pseudo-bosons}, linear or not, naturally arise in this context, and how they can be used in the computation of the pricing kernel.

ComputationFOS: Physical sciencesStatistical and Nonlinear PhysicsBlack–Scholes modelMathematical Physics (math-ph)Mathematics::Spectral Theory01 natural sciences010305 fluids & plasmasSchrödinger equationsymbols.namesakeStochastic discount factor0103 physical sciencessymbols010306 general physicsHamiltonian (quantum mechanics)Settore MAT/07 - Fisica MatematicaMathematical PhysicsStatistical and Nonlinear PhysicBosonMathematical physicsMathematics
researchProduct

Noise correlations of the ultracold Fermi gas in an optical lattice

2008

In this paper we study the density noise correlations of the two component Fermi gas in optical lattices. Three different type of phases, the BCS-state (Bardeen, Cooper, and Schieffer), the FFLO-state (Fulde, Ferrel, Larkin, and Ovchinnikov), and BP (breach pair) state, are considered. We show how these states differ in their noise correlations. The noise correlations are calculated not only at zero temperature, but also at non-zero temperatures paying particular attention to how much the finite temperature effects might complicate the detection of different phases. Since one-dimensional systems have been shown to be very promising candidates to observe FFLO states, we apply our results als…

ComputationFOS: Physical sciencesradiation pressure01 natural sciences010305 fluids & plasmaslaser coolingfermion systemsLattice (order)Laser coolingQuantum mechanicsCondensed Matter::Superconductivity0103 physical sciencesoptical lattices010306 general physicsPhysicsCondensed Matter::Quantum GasesOptical latticeCondensed matter physicsBCS theoryBCS theoryAtomic and Molecular Physics and OpticsCondensed Matter - Other Condensed MatterRadiation pressureQuasiparticleFermi gasOther Condensed Matter (cond-mat.other)
researchProduct