The Topological Open String Wavefunction

We show that, in local Calabi–Yau manifolds, the topological open string partition function transforms as a wavefunction under modular transformations. Our derivation is based on the topological recursion for matrix models, and it generalizes in a natural way the known result for the closed topological string sector. As an application, we derive results for vacuum expectation values of 1/2 BPS Wilson loops in ABJM theory at all genera in a strong coupling expansion, for various representations.     

Wavefunction Collapse and Random Walk

Wavefunction collapse models modify Schrödinger's equation so that it describes the rapid evolution of a superposition of macroscopically distinguishable states to one of them. This provides a phenomenological basis for a physical resolution to the so-called measurement problem. Such models have experimentally testable differences from standard quantum theory. The most well developed such model at present is the Continuous Spontaneous Localization (CSL) model in which a universal fluctuating classical field interacts with particles to cause collapse. One side effect of this interaction is that the field imparts energy to the particles: experimental evidence on this has led to restrictions on the parameters of the model, suggesting that the coupling of the classical field to the particles must be mass-proportional. Another side effect is that the field imparts momentum to particles, causing a small blob of matter to undergo random walk. Here we explore this in order to supply predictions which could be experimentally tested. We examine the translational diffusion of a sphere and a disc, and the rotational diffusion of a disc, according to CSL. For example, we find that the rms distance an isolated 10^–5 cm radius sphere diffuses is (its diameter, 5 cm) in (20 sec, a day), and that a disc of radius 2 10^–5 cm and thickness 0.5 10^–5 cm diffuses through 2rad in about 70 sec (this assumes the standard CSL parameter values). The comparable rms diffusions of standard quantum theory are smaller than these by a factor 10^–3±1. It is shown that the CSL diffusion in air at STP is much reduced and, indeed, is swamped by the ordinary Brownian motion. It is also shown that the sphere's diffusion in a thermal radiation bath at room temperature is comparable to the CSL diffusion, but is utterly negligible at liquid He temperature. Thus, in order to observe CSL diffusion, the pressure and temperature must be low. At the low reported pressure of 5 10^–17 Torr, achieved at 4.2°K, the mean time between air molecule collisions with the (sphere, disc) is (80, 45)min. This is ample time for observation of the putative CSL diffusion with the standard parameters and, it is pointed out, with any parameters in the range over which the theory may be considered viable. This encourages consideration of how such an experiment may actually be performed, and the paper closes with some thoughts on this subject.     

Wavefunction Collapse and Conservation Laws

It is emphasized that the collapse postulate of standard quantum theory can violate conservation of energy-momentum and there is no indication from where the energy-momentum comes or to where it goes. Likewise, in the Continuous Spontaneous Localization (CSL) dynamical collapse model, particles gain energy on average. In CSL, the usual Schrödinger dynamics is altered so that a randomly fluctuating classical field interacts with quantized particles to cause wavefunction collapse. In this paper it is shown how to define energy for the classical field so that the average value of the energy of the field plus the quantum system is conserved for the ensemble of collapsing wavefunctions. While conservation of just the first moment of energy is, of course, much less than complete conservation of energy, this does support the idea that the field could provide the conservation law balance when events occur.     

Generalized coherent states and the statistics of two-photon lasers

Stimulated two-photon emission is proposed as a possible mechanism for the generation of “generalized coherent states”, which have useful quantum properties not available in ordinary coherent states.     

Extreme statistics of complex random and quantum chaotic states

Complex random states have the statistical properties of the Gaussian and circular unitary ensemble eigenstates of random matrix theory. Even though their components are correlated by the normalization constraint, it is nevertheless possible to derive compact analytic formulas for their extreme values' statistical properties for all dimensionalities. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulas.     

Violation of Einstein locality in states with sub-poissonian statistics

The Clauser-Horne inequality is shown to be violated for a broad class of quantum states with sub-poissonian statistics. An experimental arrangement to observe non-locality of such states is proposed.     

Level statistics of near-yrast states in rapidly rotating nuclei

The nearest neighbour level spacing distribution and the Δ₃ statistic of level fluctuations associated with very high spin states (I ≳ 30) in rare-earth deformed nuclei are analysed by means of a cranked shell model. The many particle-many hole configurations created in the rotating Nilsson potential are mixed by the surface-delta two-body residual interaction. The levels in the near-yrast region show a Poisson-like level spacing distribution. As the intrinsic excitation energy U increases, the level statistics shows a gradual transition from order to chaos, reaching at U ≳ 2 MeV the Wigner distribution typical-of the Gaussian orthogonal ensemble of random matrices. This transition is caused by the residual two-body interaction. On the other hand, the level spacings between the yrast and the first excited state show a peculiar behaviour, displaying a Wigner-like distribution instead of the Poisson-like distribution seen for the other near-yrast rotational states. The lowest spacings reflect the properties of the single-particle orbits in the mean-field, and are only weakly affected by the residual two-body interaction.     

Entanglement concentration using quantum statistics

We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Because of the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.     

Wavefunction collapse and the optical theorem

The optical theorem is examined and shown to be compatible with the possibility of wavefunction collapse at the level of particle-particle interactions.     

Wavefunction localization in a binary alloy

The nature (localized or extended) of the eigenstates of a large disordered system is studied by evaluating the imaginary part of the local Green's function at the specific eigenvalues over various atomic sites. The latter is obtained from the recursion method of Haydock-Heine-Kelly. An explicit calculation on an 841-atom cluster of random binary alloy in a square lattice ensures us that this approach is able to provide the relevant answers in even larger systems. In addition to confirming the usual conjectures about localization in a random binary alloy, several interesting points show up in the result of the model calculation. For example, the localized states in the minority band are correlated to certain clustering of the minority atoms. Their specific eigenvalues, which are not easily identified from the peaks in the d.o.s., are accurately found through the |ζ|² vs. energy plots at the specific sites.     

Decoherence and Wavefunction Collapse in Quantum Measurements

Examining the notion of wavefunction collapse (WFC) in quantum measurements, which came again to be in question in the recent debate on the quantum Zeno effect, we remark that WFC is realized only through decoherence among branch waves by detection, after a spectral decomposition process from an initial object wavefunction to a superposition of branch waves corresponding to relevant measurement propositions. We improve the definition of the decoherence parameter, so as to be fitted to general cases, by which we can quantitatively estimate the degree of WFC given by detectors. Finally, we briefly discuss whether two special detector models, with very huge and very small degrees of freedom, can provoke WFC.     

Trap statistics and the gap density of states in amorphous materials

We present a one-electron theory of non-equilibrium trap occupancy in amorphous materials, with simple results for electrons in states above the equilibrium Fermi level. The density of these states can then be obtained by analysis of transient photoconductivity. Specific values are given for a-Si: H samples for energies in the range 0.55–0.40 eV below the conduction band mobility edge. We conclude that the state density there can be low, as suggested by the results of deep level transient spectroscopy.     

Polarization scrambling characteristic analysis based on density of polarization states statistics

We report a new method to deeply analyze the scrambling characteristic of polarization scramblers based on density of polarization states(DPS) statistics that makes it possible to describe the DPS distribution in detail on the whole Poincaré sphere, thus easy to locate accurately the nonuniform areas of defective polarization scramblers, which cannot be realized by existing methods. We have built a polarization scrambling system to demonstrate the advantages of our method compared with others by experiments and suggested effective evaluation indexes whose validity is well confirmed by applying to a commercial scrambler. Our conclusions are valuable for accurately analyzing and diagnosing the performance of any polarization scrambler, and quality evaluation of polarization controllers or other polarization devices.     

Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states

We consider a quantum dot in the regime of the quantum Hall effect, particularly in Laughlin states and non-Abelian Read-Rezayi states. We find the location of the Coulomb blockade peaks in the conductance as a function of the area of the dot and the magnetic field. When the magnetic field is fixed and the area of the dot is varied, the peaks are equally spaced for the Laughlin states. In contrast, non-Abelian statistics is reflected in modulations of the spacing which depend on the magnetic field.     

Wavefunction methods in electronic-structure theory of solids

The electronic-structure theory of solids is presently dominated by density-functional methods which avoid calculations of the many-body wavefunction, and instead compute directly properties of the ground state. We argue that methods which determine the many-electron wavefunctions should receive particular attention in the future. A survey is given of our present knowledge of how to calculate these wavefunctions for a solid. The accuracy we envisage compares with the one obtainable for small molecules when applying quantum-chemical methods.     

Wavefunction of Wormhole in the Einstein-Yang-Mills Theory

In this paper, the wavefunction of wormhole in the Einstein-Yang-Mills theory is presented by using the method proposed by Hawking. Analysing the wavefunction obtained, we find that the probability density of quantum wormhole at a = 0 is zero and there is the most probable radius for the ground-state wavefunction of wormhole. It indicates that the quantum wormhole is stable.