On the Sharpness and Bias of Quantum Effects

The question of quantifying the sharpness (or unsharpness) of a quantum mechanical effect is investigated. Apart from sharpness, another property, bias, is found to be relevant for the joint measurability or coexistence of two effects. Measures of bias will be defined and examples given.     

Time and Events

Time plays a special role in Standard QuantumTheory. The concept of time observable causes manycontroversies there. In Event-Enhanced Quantum Theory(EEQT) Schrodinger's differential equation is replaced by a piecewise deterministic algorithm thatdescribes also the timing of events. This allows us torevisit the problem of time of arrival in quantumtheory.     

On the Distribution of Long-Term Time Averages on Symbolic Space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in ^d are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results.     

On the Hamiltonian of the Cubic Boson Selfinteraction in Four Dimensional Space Time

In four dimensional space time a boson field with cubic selfinteraction is considered. It is shown, that if a space cutoff function is included in the interaction term, the renormalized Hamiltonian H_ren exists as a densely defined symmetric operator.     

Localization of the Poincare Group in the Spinor Space

A more general representation of the Poincare group where translation generators are generalized by P_μ= i∂_μ+kγ_μ[(l+γ₅)/2] is discussed. The corresponding spinor gauge field is studied in detail. It is shown that the Lagrangian of fermion keeps its form invariant under the above translation. An additional hidden symmetry of the Dirac field leads to a prediction of existence of an intrinsic energy-momentum for the fernlion.     

On Deriving Space–Time from Quantum Observables and States

 We prove that, under suitable assumptions, operationally motivated quantum data completely determine a space–time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined. To minimize technical complications, this is done in the example of three-dimensional Minkowski space. Received: 9 December 2002 / Accepted: 11 April 2003 Published online: 13 May 2003 Communicated by H. Araki, D. Buchholz and K. Fredenhagen     

穿越时空的对话——新课程背景下物理学史在课堂教学中的应用初探

新课程倡导课堂教学要落实"知识与技能"、"过程与方法"、"情感态度与价值观"三维教学目标.新课程背景下的课堂教学,教师如何根据教学内容,恰当地选用物理学史料,并以学生喜闻乐见的形式呈现给学生,使学生在轻松掌握知识与技能的同时,受到物理学思想方法的教育、科学态度和科学精神的熏陶,这是值得广大中学物理教师思考的一个     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

On the Problem of Emergence of Classical Space—Time: The Quantum-Mechanical Approach

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles.     

Random Walks in Space Time Mixing Environments

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.     

Two-Fluid Cosmological Models in Kaluza-Klein Space Time

In this paper we presented a class of solutions of Einstein’s field equations describing two-fluid models of the universe in a five dimensional spherical symmetric space time. In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. The radiation and matter content of the universe are in interactive phase. Also we have discussed physical and kinematical behaviors of the model.     

Space and Time: The Ongoing Quest

In this paper, I try to refute the Kantian a priorism. At the same time, I try to explain the existence of an a priori concerning space and time on the basis of contemporary neuro-physiology. This a priori is the opposite of the a-historical a priori of Kant. Concerning space and time, I argue that relativity concords with the philosophical thesis that space and time are forms of existence of matter. On the basis of this ontological principle, I support that by accepting the existence of local absolute systems of reference, it is possible to explain some paradoxes of special relativity and at the same time to refute the relativism related to the theory of Einstein.     

Sharpness and amplitude envelopes of broadband noise

This paper discusses how amplitude envelope shapes, sound-pressure level, and duration of broadband noise affect sharpness and brightness. In the first experiment, sharpness, brightness, and similarity were judged for paired stimuli by 13 subjects. The stimuli consisted of broadband noise with different types of amplitude envelopes, sound-pressure levels, and duration. Experimental results were analyzed with a multidimensional scaling technique. In addition, the second experiment measuring the point of subjective equality (PSE) of sharpness was carried out for four subjects. The results of these two experiments showed large individual differences in sharpness judgment, difficulty in brightness judgment for the stimuli used in the experiments, and influence of the amplitude envelope shapes on sharpness. The individual differences observed in sharpness judgment were explained by the differences between weights given to two psychological dimensions: loudness and subjective duration. This study forms a basis for understanding sharpness of nonsteady sounds.     

Electromagnetic Time Reversal Algorithms and Source Localization in Lossy Dielectric Media

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is proposed to localize a source density from loss-less wave-field measurements. Further, in order to recover source densities in a lossy medium, we first build attenuation operators thereby relating loss-less waves with lossy ones. Then based on asymptotic expansions of attenuation operators with respect to attenuation parameter, we propose two time reversal strategies for localization. The losses in electromagnetic wave propagation are incorporated using the Debye's complex permittivity, which is well-adopted for low frequencies (radio and microwave) associated with polarization in dielectrics.     

Spectral Localization by Gaussian Random Potentials in Multi-Dimensional Continuous Space

A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The result applies in particular to a certain class of zero-mean Gaussian random potentials, which are homogeneous with respect to Euclidean translations. More precisely, for these Gaussian random potentials the spectrum is almost surely only pure point at sufficiently negative energies or, at negative energies, for sufficiently weak disorder. The proof is based on a fixed-energy multi-scale analysis which allows for different random potentials on different length scales.