相关论文: Wave function collapse implies divergence of avera…

At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence, and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among…

In this paper, we extend original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally…

A theory is developed which attempts to reconcile the measurements of nonlocal quantum observables with special relativity and quantum mechanics. The collapse of a wave function, which coincides with a nonlocal measurement by some…

We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…

In this work, we first prove a stability theorem for traveling waves in a class of non-cooperative reaction-diffusion systems with nonlocal dispersal of equal diffusivities. Our stability criterion is in the sense that the initial…

Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the…

We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…

I present a reconstruction of general Hamiltonian action mechanics that eliminates all foundational problems of quantum mechanics. The key advance is the completion of Hamiltonian mechanics to the universal mechanics of particles based on…

A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the…

We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…

It is well-known that quantum mechanics admits two distinct evolutions: the unitary evolution, which is deterministic and well described by the Schr\"{o}dinger equation, and the collapse of the wave function, which is probablistic,…

In the present paper we investigate the influence of measurements on the quantum dynamics of degenerate Bose atoms gases in a symmetric double-well. We show that continuous measurements enhance asymmetry on the density distribution of the…

It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of…

In early days of navigation over sea and ocean it has been considered that when a ship, governed by waves, arrives as some critical distance of the global character, then this ship must absolute collapse, i.e. must fall in the nothing. Only…

In this paper, we characterize a class of solutions to the unsteady 2-dimensional flow of a van der Waals fluid involving shock waves, and derive an asymptotic amplitude equation exhibiting quadratic and cubic nonlinearities including…

The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states,…

In this paper we analyze the dispersion for one dimensional wave and Schrodinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient…

If the generalized statistics suggested by Tsallis are used in statistical mechanics, the fluctuation-dissipation theorem no longer holds. Only in the limiting case where Boltzmann statistics are recovered is the theorem applicable. In…

We consider a point particle in one dimension initially confined to a finite spatial region whose state is frequently monitored by projection operators onto that region. In the limit of infinitely frequent monitoring, the state never…