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Quantum Mechanics allows one to independently fix both the initial and final state of a single system. Novel effects occur for such systems, challenging our ideas about what time is and how it flows.
The dual Schroedinger equation is defined as replacing the imaginary number i by -1 in the original one. This paper shows that the dual equation shares the same stationary states as the original one. Different from the original one, it explicitly defines a dynamic process for a system to evolve from any state to lower energy states and eventually to the lowest one. Its power as a global optimization algorithm might be used by nature for constructing atoms and molecules. It shall be interesting to verify its existence in nature.
The following work is motivated by the conceptual problems associated with the wave-particle duality and the notion of the photon. Two simple classical models for radiation from individual emitters are compared, one based on sines with random phasejumps, another based on pulse trains. The sum signal is calculated for a varying number of emitters. The focus lies on the final signal's statistical features quantified by means of the temporal coherence function and the temporal coherence length. We show how these features might be used to experimentally differentiate between the models. We also point to ambiguities in the definition of the temporal coherence length.
Quantum decay of metastable states ('false vacua') has been proposed as a mechanism for bubble nucleation of new universes and phase transitions in the early universe. Experiments indicate the occurrence of false vacuum decay, within a region bounded by soliton domain walls that nucleate via quantum tunneling, in a highly anisotropic condensed matter system. This phenomenon provides a compelling example of false vacuum decay in the laboratory.
In this article the propagation of pointlike event probabilities in space is considered. New interpretation of Quantum Theory is formulated.
I show that the weak value theory is useful from the viewpoints of the experimentally verifiability, consistency, capacity for explanation as to many quantum paradoxes, and practical advantages. As an example, the initial state in the Hardy paradox can be experimentally verified using the weak value via the weak measurement.
I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas relate to traditional naive ideas of time and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open.
In high energy heavy ion collisions at RHIC there are important aspects of the medium induced dynamics, that are still not well understood. In particular, there is a broadening and even a double hump structure of the away-side peak appearing in azimuthal correlation studies in Au+Au collisions which is absent in p+p collisions at the same energies. These features are already present but suppressed in p+p collisions: 2 to 3 parton processes produce such structures but are suppressed with respect to 2 to 2 processes. We argue that in A+A collisions the different geometry for the trajectories of 3 as opposed to 2 particles in the final state, together with the medium induced energy loss effects on the different cross sections, create a scenario that enhances processes with 3 particles in the final state, which gives on average this double hump structure.
The ALICE experiment at the CERN's Large Hadron Collider allows the study of charmonium production in both e{sup +}e{sup -} and {mu}{sup +}{mu}{sup -} decay channels. In this paper, the first results obtained from reconstructing J/{psi} mesons in proton-proton interactions at {radical}(s) = 7 TeV are discussed. The present plans for quarkonia analyses are also mentioned.
In this work we are concerned with the minimization problem associated to the best constant C{sub n,{alpha}} in the following interpolation inequality {integral}{integral}(|u(x)|{sup {alpha}}|u(y)|{sup {alpha}}/|x-y|{sup n-2})dxdy{<=}C{sub n,{alpha}}||{nabla}{psi}||{sub L{sup 2}}{sup n{alpha}-(n+2)}||{psi}|| {sub L{sup 2}}{sup (n+2)-(n-2){alpha}}, u is an element of H{sup 1}(R{sup n}) for 2{<=}{alpha}<1+4/(n-2) and n{>=}3. The corresponding variational problem is equivalent to the problem of existence of a ground state solution to the nonlinear non-local elliptic equation -{Delta}u+{omega}u-(|x|{sup -(n-2)}*|u|{sup {alpha}})|u|{sup {alpha}-2}u = 0. We show that the ground state solution is unique and its mass parallel u parallel {sub L{sup 2}}{sup 2} determines the best constant C{sub n,{alpha}}. As a consequence of the above results, we obtain sharp sufficient condition for global existence for the L{sup 2}-critical Hartree equation.
We propose a controller based coupling design for engineering synchronization in chaotic oscillators for unidirectional as well as bi-directional mode. In the synchronization regimes, it is possible to amplify/ attenuate a chaotic attractor with respect to other chaotic attractors. Numerical examples are presented for a Lorenz system, a Roessler oscillator, and a Sprott system. Physical implementation of the scheme is done in electronic circuit to design the controller for verification of the theory.
We present a new theory of the anharmonicity of nonlinear oscillations that are exhibited by many physical systems. New physical quantities are introduced that describe the departure from linear or harmonic behavior and as far as extremely anharmonic situations. In order to solve the nonlinear phase equation, the key notion of our theory, which controls the anharmonic behavior, a new and fascinating nonlinear trigonometry is designed. These results provide a general and accurate yet compact description of such signals, by far better than the Fourier description, both quantitatively and qualitatively and will benefit many application fields.
We show the asymptotic completeness for two-body quantum systems in an external electric field asymptotically non-zero constant in time. One of the main ingredients of this paper is to give some propagation estimates for physical propagators generated by time-dependent Hamiltonians which govern the systems under consideration.
Retrocausation has been postulated in physical systems and observed in animate systems. The experiments described here extend methods used in human experiments to systems that are inanimate. One random-event generator, the controller-REG, was used to shut off a second REG, the subject-REG, at a random time. The output of the subject-REG was accumulated over several runs, each consisting of hundreds of trials, to look for a change in the randomness of its output bit stream in advance of the subject-REGs shut off. For the first three runs large changes were observed during the last second before shut off, changes of approximately 1 bit in 40 that exceeded odds against chance of 1 million to 1. Variations and later an exact replication of the early results failed to show the changes observed in the first three runs. This failure to replicate is an indication that there is an additional uncontrolled variable that must be taken into account, quite possibly the intention and enthusiasm of the experimenters. That addition leads to the question as to whether the subject-REG was subject to advance influence from its impending shut off, or instead whether its output was in a superposition of different states until the operator observed the results. The observation would then have caused a collapse of the superposition into a fixed state, like the collapse of quantum mechanical wavefunction. In either case, a retroactive influence was clearly in evidence.
We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power (5/3).
The linear and nonlinear properties of low-frequency electrostatic excitations of charged dust particles (or defects) in a dense collisionless, unmagnetized Thomas-Fermi plasma are investigated. A fully ionized three-component model plasma consisting of electrons, ions, and negatively charged massive dust grains is considered. Electrons and ions are assumed to be in a degenerate quantum state, obeying the Thomas-Fermi density distribution, whereas the inertial dust component is described by a set of classical fluid equations. Considering large-amplitude stationary profile travelling-waves in a moving reference frame, the fluid evolution equations are reduced to a pseudo-energy-balance equation, involving a Sagdeev-type potential function. The analysis describes the dynamics of supersonic dust-acoustic solitary waves in Thomas-Fermi plasmas, and provides exact predictions for their dynamical characteristics, whose dependence on relevant parameters (namely, the ion-to-electron Fermi temperature ratio, and the dust concentration) is investigated. An alternative route is also adopted, by assuming weakly varying small-amplitude disturbances off equilibrium, and then adopting a multiscale perturbation technique to derive a Korteweg-de Vries equation for the electrostatic potential, and finally solving in terms for electric potential pulses (electrostatic solitons). A critical comparison between the two methods reveals that they agree exactly in the small-amplitude, weakly superacoustic limit. The dust concentration (Havnes) parameter h=Z{sub d0}n{sub d0}/n{sub e0} affects the propagation characteristics by modifying the phase speed, as well as the electron/ion Fermi temperatures. Our results aim at elucidating the characteristics of electrostatic excitations in dust-contaminated dense plasmas, e.g., in metallic electronic devices, and also arguably in supernova environments, where charged dust defects may occur in the quantum plasma regime.
We present a new conformally invariant higher order operator on the n-dimensional sphere, acting on functions with values in the representation with highest weight ((5/2),(1/2),...,(1/2)). The construction uses the spectrum generating method by Branson, Orsted and Olafsson and is a higher spin analog of the construction of conformally invariant powers of Dirac operators by Liu and Ryan and of the operators on spin-forms constructed recently by Hong.
Complete information on the behavior of zonal flows in turbulence systems is coded in the turbulent stress response to the respective flow pattern. We show that turbulence stress response functionals containing only the linear first order wavenumber dependence on the flow pattern result in unstable structures up to the system size. A minimal augmentation to reproduce the flow patterns observed in turbulence simulations is discussed.