共查询到20条相似文献,搜索用时 656 毫秒
1.
This paper aims at conducting an analysis of various uncertainty principles from a topological point of view where the notion of symplectic capacity plays a key role. The existence of symplectic capacities follows from a deep theorem of symplectic topology, Gromov’s non-squeezing theorem, which was discovered in the mid 1980’s, and which has led to numerous developments whose applications to Physics are not fully understood or exploited at the time of writing. We will show that the notion of symplectic non-squeezing contains, as a watermark, not only the Robertson–Schrödinger uncertainty relations (and a classical version thereof), but also Hardy’s uncertainty principle for a function and its Fourier transform. This observation will allow us to formulate the characterization of positivity for density matrices in a topological way. We also address some open questions and conjectures, whose solution cannot be given at the present time due to the lack of a sufficiently developed mathematical theory. 相似文献
2.
In this Letter, a new local linear prediction model is proposed to predict a chaotic time series of a component x(t) by using the chaotic time series of another component y(t) in the same system with x(t). Our approach is based on the phase space reconstruction coming from the Takens embedding theorem. To illustrate our results, we present an example of Lorenz system and compare with the performance of the original local linear prediction model. 相似文献
3.
Livia Corsi Guido Gentile Michela Procesi 《Communications in Mathematical Physics》2011,302(2):359-402
The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt
series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by
following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations
between contributions of the same perturbation order. In turn, this is due to symmetries in the problem. Such symmetries are
easily visualised in action-angle coordinates, where the KAM theorem is usually formulated by exploiting the analogy between
Lindstedt series and perturbation expansions in quantum field theory and, in particular, the possibility of expressing the
solutions in terms of tree graphs, which are the analogue of Feynman diagrams. If the unperturbed system is isochronous, Moser’s
modifying terms theorem ensures that an analytic quasi-periodic solution with the same Diophantine frequency vector as the
unperturbed Hamiltonian exists for the system obtained by adding a suitable constant (counterterm) to the vector field. Also
in this case, one can follow the alternative approach of studying the perturbation expansion for both the solution and the
counterterm, and again convergence of the two series is obtained as a consequence of deep cancellations between contributions
of the same order. In this paper, we revisit Moser’s theorem, by studying the perturbation expansion one obtains by working
in Cartesian coordinates. We investigate the symmetries giving rise to the cancellations which makes possible the convergence
of the series. We find that the cancellation mechanism works in a completely different way in Cartesian coordinates, and the
interpretation of the underlying symmetries in terms of tree graphs is much more subtle than in the case of action-angle coordinates. 相似文献
4.
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage. 相似文献
5.
An asymptotic solving method for the periodic solution of a class of disturbed nonlinear evolution equation 下载免费PDF全文
<正>A class of disturbed evolution equation is considered using a simple and valid technique.We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation.Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method.We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis. 相似文献
6.
Taken's delay embedding theorem states that a pseudo state-space can be reconstructed from a time series consisting of observations of a chaotic process. However, experimental observations are inevitably corrupted by measurement noise, which can be modelled as Additive White Gaussian Noise (AWGN). This Letter analyses time series prediction in the presence of AWGN using the triangle inequality and the mean of the Nakagami distribution. It is shown that using more delay coordinates than those used by a typical delay embedding can improve prediction accuracy, when the mean magnitude of the input vector dominates the mean magnitude of AWGN. 相似文献
7.
Sebastian Raubitzek Thomas Neubauer Jan Friedrich Andreas Rauber 《Entropy (Basel, Switzerland)》2022,24(5)
We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically-interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and compared to a cubic spline interpolation and a linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches. Further, the results suggest that the variance of second derivatives along a given phase space trajectory is a valuable tool for phase space analysis of non-model time series data, and we expect it to be useful for future research. 相似文献
8.
9.
Using the nonrenormalization theorem and Pohlmeyer's theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess–Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kähler potential. 相似文献
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11.
J. Carrasquilla-Alvarez R. Castaneda J. Garcia-Sucerquia M.A. Schofield M. Beleggia Y. Zhu G. Matteucci 《Optik》2008,119(3):127-133
The possibility to characterize the coherence properties of an electron source is presented. The method, based on the determination of centered-reduced moments of the beam spot, allows the evaluation of both amplitude and phase of the complex degree of spatial coherence. The experimental results are in agreement with a different approach based on the Fourier analysis and with calculations according to the Van Cittert—Zernike theorem. 相似文献
12.
Q-exponential distributions play an important role in nonextensive statistics. They appear as the canonical distributions, i.e. the maximum generalized q-entropy distributions under mean constraint. Their relevance is also independently justified by their appearance in the theory of superstatistics introduced by Beck and Cohen. In this paper, we provide a third and independent rationale for these distributions. We indicate that q-exponentials are stable by a statistical normalization operation, and that Pickands’ extreme values theorem plays the role of a CLT-like theorem in this context. This suggests that q-exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold. Moreover we give an asymptotic connection between excess distributions and maximum q-entropy. We also highlight the role of Generalized Pareto Distributions in many applications and present several methods for the practical estimation of q-exponential parameters. 相似文献
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14.
We consider the use of qutrits in a two way deterministic quantum cryptographic protocol which exhibits a higher level of security. We analyse the security of the protocol in the context of the Intercept Resend Strategy. The protocol which transmits a qutrit is naturally limited to not utilising all the available maximally overlapping basis due to a no go theorem not unlike the universal-NOT. We further propose another protocol to generalise the protocol above against the no-go theorem. 相似文献
15.
The plaquette expansion, a general non-perturbative method for calculating the properties of lattice Hamiltonian systems, is established up to the first two orders for an arbitrary system. This method employs an expansion of the Lanczos coefficients, the tridiagonal Hamiltonian matrix elements or equivalently the continued fraction coefficients of the resolvent, in a descending series in the size of the system. The coefficients of this series are formed from the low order cumulants or connected Hamiltonian moments. The lowest order approximation in the plaquette expansion corresponds to a gaussian model which is a consequence of the central limit theorem. The first nontrivial order yields a model with a spectrum on a bounded energy interval, becoming asymptotically uniform in the thermodynamic limit. 相似文献
16.
E. Gutkin 《Letters in Mathematical Physics》1979,3(3):185-192
We prove a theorem for the tensor product of representations of the holomorphic discrete series analogous to the classical theorem of Clebsch-Gordan and give an asymptotic formula for corresponding coefficients of Clebsch-Gordan. For small groups we compute the coefficients explicitly.Partially supported by NSF Grant MCS 78-01826. 相似文献
17.
Thomas Marlow 《Annals of Physics》2006,321(5):1103-1125
We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different approaches to formalising multi-time measurements in quantum theory. The standard approach consists of describing an ordered series of measurements in terms of history propositions with non-additive ‘probabilities.’ The non-standard approach consists of defining multi-time measurements to consist of sets of exclusive and exhaustive history propositions and recovering the single-time exclusivity of results when discussing single-time history propositions. We analyse whether such history propositions can be consistent with Bayes’ rule. We show that certain class of histories are given a natural Bayesian interpretation, namely, the linearly positive histories originally introduced by Goldstein and Page. Thus, we argue that this gives a certain amount of interpretational clarity to the non-standard approach. We also attempt a justification of our analysis using Cox’s axioms of probability theory. 相似文献
18.
Basu A Joanny JF Jülicher F Prost J 《The European physical journal. E, Soft matter》2008,27(2):149-160
We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the
single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells.
Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the
constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage
of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from
equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation
function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities. 相似文献
19.
Based on the 2 × 2 cross-spectral density matrix, the van Cittert-Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization. 相似文献
20.
B. Schulz 《Annalen der Physik》2009,18(4):231-270
In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark about Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on the theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden‐variable model. Finally, we mention that this theory could perhaps be relativistically extended and useful for the formulation of quantum mechanics in curved space‐times. 相似文献