共查询到20条相似文献,搜索用时 30 毫秒
1.
C. Wetterich 《Annals of Physics》2011,(8):2243-2293
We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function qτ(t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as . The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions. 相似文献
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C. Wetterich 《Foundations of Physics》2012,42(11):1384-1443
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions p τ (t) at a given time t obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_{\tau}(t)=\pm \sqrt{p_{\tau}(t)}$ . We establish a map to quantum physics and the Schr?dinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time. 相似文献
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We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η1,η2〉λ,ν and |?1,?2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established. 相似文献
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The statistical properties of the return intervals τq between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τq for different thresholds q. Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function with γ≈0.31 under the significance level of 5%, where is the mean return interval. The investigation of the conditional probability distribution Pq(τ|τ0) and the mean conditional return interval 〈τ|τ0〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈τ|τ0〉 after a cluster of n intervals and the fluctuation F(l) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals. 相似文献
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We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution Pq(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution Pq(τ|τ0), the mean conditional interval 〈τ|τ0〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P±(t) and find that P−(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets. 相似文献
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Y.C Ratnakaram D Thirupathi Naidu J.L Rao 《Journal of Physics and Chemistry of Solids》2003,64(12):2487-2495
The effect of mixed alkalis on the optical absorption spectra of Tm3+ in xNa2O·(30−x)K2O·70B2O3 glasses has been studied. The optical band gap values (Eopt) for both direct and indirect transitions have been obtained using Davis and Mott theory. Spectroscopic parameters like Racah (E1, E2 and E3), spin-orbit (ξ4f) and Judd-Ofelt intensity parameters (, and ) have been calculated for different x values. Radiative transition probabilities (Arad), radiative lifetimes (τR), branching ratios (β), integrated absorption cross sections (Σ) and multiphonon relaxation rates (WMPR) are calculated for certain excited states of Tm3+ ion. The observed trends in the above parameters as a function of x in these borate glasses have been discussed keeping in view the effect of mixed alkalies in borate glasses. Certain potential lasing transitions have been identified for laser action among the various transitions of Tm3+ in these mixed alkali borate glasses. 相似文献
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C.Richard Quade 《Journal of Molecular Spectroscopy》2003,219(2):186-190
Vibration-internal rotation-rotation interaction theory has been used to calculate the τ-dependence of F, the reduced kinetic energy coefficient for internal rotation for CH3OH from molecular structure. The leading term is as a fraction of F0. Smaller terms are and then and for the symmetry breaking terms of the vibrationally distorted molecule. These terms have not been included previously in torsion-rotation anaylses for CH3OH but should be compared with the fractional uncertainty in F0 of ±7×10−7. A rough estimate of the τ-independent vibrational contributions to F0 is of the order 4% with the largest contributors being the COH bend and OH stretch. 相似文献
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Miriam Lemanska 《Physica A》2008,387(12):2719-2735
A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S∞=limSk, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions pi(t0), where pi(t)=ni(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution pi is given by the equation −lnpi+a+eib=0 common to Sk and S∞ systems with the same value of a and b. The term a=β−1ae, where ae is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated. 相似文献
11.
Ali Mostafazadeh 《Annals of Physics》2004,309(1):1-48
With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂t2+D)ψ(t)=0, where and D is a positive-definite operator acting in a Hilbert space . In particular, we determine all the positive-definite inner products on the space of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in . Among these is a particular choice that generates t-translations in and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in , and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in , show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint. 相似文献
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Richard Jozsa 《Annals of Physics》2003,306(2):241-279
Pell’s equation is x2−dy2=1, where d is a square-free integer and we seek positive integer solutions x,y>0. Let (x0,y0) be the smallest solution (i.e., having smallest ). Lagrange showed that every solution can easily be constructed from A so given d it suffices to compute A. It is known that A can be exponentially large in d so just to write down A we need exponential time in the input size . Hence we introduce the regulator R=lnA and ask for the value of R to n decimal places. The best known classical algorithm has sub-exponential running time . Hallgren’s quantum algorithm gives the result in polynomial time with probability . The idea of the algorithm falls into two parts: using the formalism of algebraic number theory we convert the problem of solving Pell’s equation into the problem of determining R as the period of a function on the real numbers. Then we generalise the quantum Fourier transform period finding algorithm to work in this situation of an irrational period on the (not finitely generated) abelian group of real numbers. This paper is intended to be accessible to a reader having no prior acquaintance with algebraic number theory; we give a self-contained account of all the necessary concepts and we give elementary proofs of all the results needed. Then we go on to describe Hallgren’s generalisation of the quantum period finding algorithm, which provides the efficient computational solution of Pell’s equation in the above sense. 相似文献
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André L.M. Vilela 《Physica A》2009,388(19):4171-4178
We consider the majority-vote model with noise in a network of social interactions for a system with two classes of individuals, class σ and class τ. For the two-agent model each class has its own dynamics, with individuals of σ class being influenced by neighbors of both classes, while the individuals of type τ are influenced only by neighbors of that class. We use Monte Carlo simulations and finite-size scaling techniques to estimate the critical properties of the system in the stationary state. The calculated values of the critical noise parameters, and , allow us to identify five distinct regions in the phase diagram on the qτ-qσ plane. The critical exponents for each class are the same and we conclude that the present model belongs to the same universality class as the two-dimensional Ising model. 相似文献
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Taking Cu as an example, the surface stress and surface energy in three low index surfaces and two families of representative surfaces and belong to [0 0 1]- and -rotating axis respectively, have been calculated using MEAM. For the three low index surfaces, the decrease in the surface energy is small after relaxation, while the surface stresses in the surface planes τxx and τyy show opposite changes (decreasing and increasing) for inward and outward relaxations. The resulting relaxation direction is related to the normal stress τzz before relaxation. For the surfaces of the and families, with the increasing angle α (between the and (1 0 0) planes, and between and (0 0 1) planes, respectively), the surface stress and surface energy go through an oscillatory change. The surface stress and surface energy are symmetric about the planes (1 0 0), (1 1 0) and (0 1 0) at α=0°, 45° and 90°, and about the planes (0 0 1) and (1 1 0) at α=0° and 90° respectively, due to crystal symmetry. 相似文献
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M.O. Goerbig P. Lederer C. Morais Smith 《Physica E: Low-dimensional Systems and Nanostructures》2006,34(1-2):57
Most states of the fractional quantum Hall effect may be interpreted in terms of an integral quantum Hall effect of weakly-interacting quasiparticles (composite fermions). The recently discovered state does not belong to these states because its formation is due to the residual interactions between composite fermions, which become relevant when the composite-fermion levels are only partially filled. We have derived a model of interacting composite fermions, which reveals the self-similarity of the fractional quantum Hall effect and which allows for a systematic study of higher generations of composite fermions. Here, we derive the form of the interaction potential between these hierarchical composite fermions and provide some stability criteria for such states. 相似文献
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We construct the explicit formulation of the probabilistically perfect quantum cloning machine that perfectly duplicates the input states chosen from the special set consisting of the linearly independent and nonorthogonal quantum states with 〈φi ∣φj〉 = r ∈ (0, 1)(i ≠ j). The success probabilities of cloning the input states are equal and maximal. As two examples, we present the explicit transformations of the optimal 1 → 2 probabilistically perfect quantum cloning of the real states in 2 and 3 dimensions. The success probabilities of each of two cloning machines are equal and maximal. 相似文献
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We report the results of a comprehensive study of weak localization and electron-electron interaction effects in disordered V1−xPdx alloys whose compositions are close to the (low Tc) A15 V3Pd compound. Magnetoresistivity and zero field resistivity have been measured within the temperature range 1.5≤T≤300 K. The low-temperature resistivity obeys a law, which is explained by electron-electron interaction. We have determined the electron-phonon scattering time (τe-ph) for V1−xPdx alloys. Our results indicate an anomalous electron-phonon scattering rate obeying quadratic temperature dependence. This observation is interpreted by the existing theories of electron-phonon interactions. 相似文献
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We study statistical properties of the Hamiltonian generating phase state. Using the generalized Hellmann-Feynman theorem for ensemble average, we derive its mean energy and find the ratio of the mean energies contributed from the term a†a to that from . The relation on the entropy-variation with respect to the dynamic parameters ω and κ is also examined. 相似文献
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Firstly, we investigate the necessary and sufficient conditions that an entangled channel of n-qubits should satisfy to carry out perfect teleportation of an arbitrary single qubit state and dense coding. It is shown that the sender can transmit two classical bits of information by sending one qubit. Further, the case of high-dimension quantum state is also considered. Utilizing n-qudit state as quantum channel, it is proposed that the necessary and sufficient conditions are in all to teleport an arbitrary single qudit state. The sender can transmit 2log2d classical bits of information to the receiver conditioned on the constraints. 相似文献