A Local Quantum Version of the Kolmogorov Theorem

Consider in L²(^l) the operator family H():=P₀(,)+Q₀. P₀ is the quantum harmonic oscillator with diophantine frequency vector , Q₀ a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and . Then there exists *>0 with the property that if ||<* there is a diophantine frequency () such that all eigenvalues E_n(,) of H() near 0 are given by the quantization formula where is an l-multi-index.Supported in part by NSF grant DMS-0204985.     

Quantum probabilities,operators of state preparation,and the principle of superposition

An integrated view concerning the probabilistic organization of quantum mechanics is first obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar space-time structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth probability-trees, complex constructs with treelike space-time support. Though it is strictly entailed by confrontation with the abstract theory of probabilities as it now stands, the construct of a quantum mechanical probability treetransgresses this theory. It indicates the possibility of an extended abstract theory of probabilities: Quantum mechanics appears to be neither a normal probabilistic theory nor an abnormal one, but a pioneering particular realization of afuture extended abstract theory of probabilities. The integrated perception of the probabilistic organization of quantum mechanics removes the current identifications of spectral decompositions of one state vector, with superpositions of several state vectors. This leads to the definition of operators of state preparation and of the calculus with these and to a clear understanding of the physical significance of the principle of superposition. Furthermore, a complement to the quantum theory of measurements is obtained.     

Quantum graph vertices with permutation-symmetric scattering probabilities

Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix U. Observing that if U has at most two eigenvalues, then the scattering matrix S(k) of the vertex is a linear combination of the identity matrix and a fixed Hermitian unitary matrix, we construct vertex couplings with this property: For all momenta k, the transmission probability from the j-th edge to ?-th edge is independent of (j,?), and all the reflection probabilities are equal. We classify these couplings according to their scattering properties, which leads to the concept of generalized δ- and δ^′-couplings.     

Quantum Zeno and anti-Zeno effects measured by transition probabilities

Using numerical calculations, we compare the transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For various distribution functions, we find the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decay freezing occurs only under frequent modulations as the pulse delay approaches zero. In the large pulse-delay region, however, the transition probabilities under frequent modulations are highest among the three control methods.     

Quantum logic of sequential events and their objectivistic probabilities

A propositional calculus for quantum mechanical systems is presented which formalizes sequential connectives and then and or then for yes-no experiments in the framework of complex Hilbert space. Properties of these connectives are compared with some well-known lattice-theoretical results in quantum logic. Probabilities and objectivization versus the Copenhagen interpretation are discussed in connection with Young's two-slit experiment.     

Quantum watermarking based on threshold segmentation using quantum informational entropy

We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image. The core idea of this scheme is to embed information into object and background of cover image in different ways. First, a threshold method adopting the quantum informational entropy is employed to determine a threshold value. The threshold value can then be further used for segmenting the cover image to a binary image, which is an authentication key for embedding and extraction information. By a careful analysis of the quantum circuits of the scheme, that is, translating into the basic gate sequences which show the low complexity of the scheme. One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image. Furthermore, the analyses of peak signal-to-noise ratio, histogram and capacity of the scheme are also provided.     

Quantum particles from coarse grained classical probabilities in phase space

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.     

用量子力学方法计算H+H2碰撞的反应几率

利用量子力学耦合通道扭曲波近似法(CCDWA)和三种势能面计算了H+H2碰撞的反应几率,结果发现在相同的势能面下利用CCDWA方法计算的反应几率和公认较好的计算结果符合很好,不同势能面共线势垒高度的差别将引起反应几率的不同.     

Kolmogorov turbulence, Anderson localization and KAM integrability

A modified Shastry-Sutherland model with fourth-nearest-neighbor dimerization is studied with strong coupling perturbation theory. One-triplet excitations are calculated up to the second order. Bose-Einstein condensation of one-triplet excitations may induce different ordered states, i.e. collinear antiferromagnetic state, Néel state or incommensurate state when the gap closes by changing the physical parameters or by an external magnetic field. Two-triplet bound states in the S = 1 and S = 2 channels are shown to exist around the symmetric lines of K _x = ±K _y and K _x ± K _y = ±??. For ferromagnetic dimer-dimer interaction, the energies of the bound states in the S = 1 (S = 2) channel lie above (below) the two-triplet continuum. By calculating the existence region, the degeneracy, the symmetry and the dispersion relation, a whole image and main features of the bound states are obtained. Experimental results of (CuX)LaNb₂O₇ with X = Cl, Br are interpreted.     

Present,predicted, and hidden probabilities

The general properties of measurements in microphysics are studied and the three types of probabilities that, according to the authors, appear in wave mechanics are set up. Such a distinction, together with the principle of the localization of the corpuscle as was laid down at the very introduction of the theory of the double solution, provides a good grasp of certain phenomena whose explanation according to the usual theory (which makes no use of permanent localization and where the three types of probabilities are intermingled) leads to paradoxical or self-contradictory situations.     

Identical particles, projectors and probabilities

In this Letter we reanalyze the old problem of the probability interpretation of the wave function in the case of identical particles. It is shown that, although the construction of observable single particle position (or momentum) operators is not easy nor natural, it is possible to bypass the problem through the construction of projectors that make probability computations completely systematic, easy to understand and adequate to the spirit of Quantum Mechanics.     

Semiconductor lasers and Kolmogorov spectra

We make a prima facie case that there could be distinct advantages to exploiting a new class of finite flux equilibrium solutions of the quantum Boltzmann equation in semiconductor lasers.     

Quantum Cryptography,Quantum Communication,and Quantum Computer in a Noisy Environment

First, we study several information theories based on quantum computing in a desirable noiseless situation. (1) We present quantum key distribution based on Deutsch’s algorithm using an entangled state. (2) We discuss the fact that the Bernstein-Vazirani algorithm can be used for quantum communication including an error correction. Finally, we discuss the main result. We study the Bernstein-Vazirani algorithm in a noisy environment. The original algorithm determines a noiseless function. Here we consider the case that the function has an environmental noise. We introduce a noise term into the function f(x). So we have another noisy function g(x). The relation between them is g(x) = f(x) ± O(??). Here O(??) ? 1 is the noise term. The goal is to determine the noisy function g(x) with a success probability. The algorithm overcomes classical counterpart by a factor of N in a noisy environment.     

Fractional backward Kolmogorov equations

This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equation in the fractal time whose coefficient functions are independent of time, its solution is equal to the transfer probability density function of the subordinated process X(Sα(t)), the subordinator Sα(t) is termed as the inverse-time α-stable subordinator and the process X(τ) satisfies the corresponding time homogeneous Ito stochastic differential equation.