Mathematical Physics Research Papers - Academia.edu (original) (raw)

The open string ending on a D-brane with a constant B-field in a pp-wave Ramond-Ramond background is exactly solvable. The theory is controlled by three dimensionful parameters: α ′ , the mass parameter (RR background times the lightcone... more

The open string ending on a D-brane with a constant B-field in a pp-wave Ramond-Ramond background is exactly solvable. The theory is controlled by three dimensionful parameters: α ′ , the mass parameter (RR background times the lightcone momentum) and the B-field. We quantize the open string theory and determine the full noncommutative structure. In particular, we find a fully noncommutative phase space whose noncommutativity depends on all these parameters. The lightcone Hamiltionian is obtained, and as a consequence of the nontrivial commutation relations of the theory, new features of the spectrum are noted. Various scaling limits of the string results are considered. Physical implications are discussed.

A brief overview 1 of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the... more

A brief overview 1 of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the remarkable intuition that John Wheeler had. Discussion is organized at two levels. The the main text provides a bird's eye view of the subject that should be accessible to nonexperts. Appendices address conceptual and technical issues that are often raised by experts in loop quantum gravity and string theory.

The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one... more

The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one sense or another are made up of infinitely many line segments, with specific attention to the "infinite staircase" and to the Koch snowflake, for both of which we develop explicit formulas for the mapping function and explain how one can use standard mathematical software to generate corresponding graphics. We also discuss a number of open questions suggested by these considerations, some of which are related to differentials on hyperelliptic surfaces of infinite genus.

The charged quantum geometry of mass-ENERGY-Matter - developed from the foundational postulate that quantised angular momenta of Planck's constant is in fact reflective of an equilateral mass-energy geometry from which all 2d immaterial... more

The charged quantum geometry of mass-ENERGY-Matter - developed from the foundational postulate that quantised angular momenta of Planck's constant is in fact reflective of an equilateral mass-energy geometry from which all 2d immaterial EM fields and 3D material particles are created.

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We focus on integrable systems with two degrees of freedom that are integrable in the Liouville sense and are obtained as real and imaginary parts of a polynomial (or entire) complex fimction in two complex variables. We propose... more

We focus on integrable systems with two degrees of freedom that are integrable in the Liouville sense and are obtained as real and imaginary parts of a polynomial (or entire) complex fimction in two complex variables. We propose definitions of the actions for such systems (which are not of the Arnol'd-Liouville type). We show how to compute the actions from a complex Hamilton-3acobi equation and apply these techniques to several examples including those recently considered in relation to perturbations of the Ruijsenaars-Schneider system. These examples introduce the crucial problem of the semiclassical approach to the corresponding quantum systems.

The possible process of creation/annihilation of traversable wormholes in the model with phantom (ghost) scalar field is described. It is shown that such process can be realized only for some special choice of a potential energy, in... more

The possible process of creation/annihilation of traversable wormholes in the model with phantom (ghost) scalar field is described. It is shown that such process can be realized only for some special choice of a potential energy, in particular, for the Sine-Gordon potential.

To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to these observers,... more

To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to these observers, and show that, for any locally inertial frame, the speed of a freely falling material particle is always less than the speed of light at the Schwarzschild black hole surface. 2 1

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics... more

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioral sciences teach us that random variables measuring the same content (the answer to the same Yes or No question) may vary, if measured jointly with other random variables. Alice and Bob raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant outcomes and to estimate correlations. Marginal expectations, estimated using these final samples, depend on distant settings. Therefore, a system of random variables measured in Bell tests is inconsistently connected and it should be analyzed using a Contextuality-by-Default approach, what is done for the first time in this paper. The violation of Bell inequalities and inconsistent connectedness may be explained...

A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data... more

A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data collection of numbers. Both are universal in the sense that FLL only depends on the numbers of letters in the alphabet, whereas BL only depends on the number of digits in the base of the number system. The existence of these types of universal laws appears counter-intuitive. Nonetheless both describe data very well. Relations to some earlier works are given. FLL predicts that an English author on the average starts about 16 out of 100 words with the English letter 't'. This is corroborated by data, yet an author can freely write anything. Fuller implications and the applicability of FLL remain for the future.

The correlated metal UCoGe is a weak itinerant ferromagnet with a Curie temperature T C = 3 K and a superconductor with a transition temperature T s = 0.6 K. We review its basic thermal, magnetic  on the macro and microscopic scale  and... more

The correlated metal UCoGe is a weak itinerant ferromagnet with a Curie temperature T C = 3 K and a superconductor with a transition temperature T s = 0.6 K. We review its basic thermal, magnetic  on the macro and microscopic scale  and transport properties, as well as the response to high pressure. The data unambiguously show that superconductivity and ferromagnetism coexist below T s = 0.6 K and are carried by the same 5f electrons. We present evidence that UCoGe is a p-wave superconductor and argue that superconductivity is mediated by critical ferromagnetic spin fluctuations.

We have examined the fall-off of power spectra at high frequencies as a possible means of distinguishing systems exhibiting deterministic chaos from systems subject to noise. It has been conjectured for some time that deterministic... more

We have examined the fall-off of power spectra at high frequencies as a possible means of distinguishing systems exhibiting deterministic chaos from systems subject to noise. It has been conjectured for some time that deterministic systems with a small number of degrees of freedom should have power spectra that fall off faster than any inverse power of the frequency while, on the other hand, spectra from systems subject to noise should decay via a power law.l, 2

The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero... more

The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero temperature by means of well-controlled numerical procedures. For selected values of the unique coupling parameter U the restricted phase diagrams (based on all the periodic configurations of localized particles (ions) with period not greater than 16 lattice constants, typically) have been constructed in the grand-canonical ensemble. Then these diagrams have been translated into the canonical ensemble. Compared to the diagrams obtained in other studies our ones contain more details, in particular they give better insight into the way the mixtures of periodic phases are formed. Our study has revealed several families of new characteristic phases like the generalized most homogeneous and the generalized crenel phases, a first example of a structural phase transition and a tendency to build up an additional symmetry - the hole-particle symmetry with respect to the ions (electrons) only, as U decreases.

Fluids in porous media are commonly studied with analytical or simulation methods, usually assuming that the host medium is rigid. By evaluating the substrate’s response (relaxation) to the presence of the fluid we assess the error... more

Fluids in porous media are commonly studied with analytical or simulation methods, usually assuming that the host medium is rigid. By evaluating the substrate’s response (relaxation) to the presence of the fluid we assess the error inherent in that assumption. One application is a determination of the ground state of 3He in slit and cylindrical pores. With the relaxation, there results a much stronger cohesion than would be found for a rigid host. Similar increased binding effects of relaxation are found for classical fluids confined within slit pores or nanotube bundles.

In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of... more

In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs. *

By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Lévy noise. After shortly review recent results obtained with different approaches on the time characteristics of the... more

By using the backward fractional Fokker-Planck equation we investigate the barrier crossing event in the presence of Lévy noise. After shortly review recent results obtained with different approaches on the time characteristics of the barrier crossing, we derive a general differential equation useful to calculate the nonlinear relaxation time. We obtain analytically the nonlinear relaxation time for free Lévy flights and a closed expression in quadrature of the same characteristics for cubic potential.

This paper is about adiabatic transport in quantum pumps. The notion of "energy shift", a self-adjoint operator dual to the Wigner time delay, plays a role in our approach: It determines the current, the dissipation, the noise and the... more

This paper is about adiabatic transport in quantum pumps. The notion of "energy shift", a self-adjoint operator dual to the Wigner time delay, plays a role in our approach: It determines the current, the dissipation, the noise and the entropy currents in quantum pumps. We discuss the geometric and topological content of adiabatic transport and show that the mechanism of Thouless and Niu for quantized transport via Chern numbers cannot be realized in quantum pumps where Chern numbers necessarily vanish.

Smooth 2-surfaces with pseudo-Riemannian metric are considered, that is, ones with quadratic form in the tangent bundle that is not positive-definite. Degeneracy points of the form are said to be parabolic. Geodesic lines induced by this... more

Smooth 2-surfaces with pseudo-Riemannian metric are considered, that is, ones with quadratic form in the tangent bundle that is not positive-definite. Degeneracy points of the form are said to be parabolic. Geodesic lines induced by this pseudo-Riemannian metric in a neighbourhood of typical parabolic points are considered, their phase portraits are obtained and extremal properties are investigated. Bibliography: 23 titles.

Semi-insulating, undoped, Liquid Encapsulated Czochralski (SI-U LEC) GaAs detectors have been irradiated with 24 GeV/c protons at the fluence of 5.6× 1013 p/cm 2. The detector charge collection efficiency, cce, for both electrons and... more

Semi-insulating, undoped, Liquid Encapsulated Czochralski (SI-U LEC) GaAs detectors have been irradiated with 24 GeV/c protons at the fluence of 5.6× 1013 p/cm 2. The detector charge collection efficiency, cce, for both electrons and holes is remarkably reduced after irradiation while the reverse current increases. The effect of annealing the detectors at temperatures ranging from 220 °C to 280 °C has been seen to reduce the reverse current and to increase the electron cce, while the recovery of the hole cce is negligible in irradiated detectors. Deep electron traps have been followed in their evolution with the heat treatment temperature by P-DLTS and C-V measurements. They recover by increasing the heat treatment temperature and this can explain the restoration observed in electron cce.

We show that the partition function of free Maxwell theory on a generic Euclidean fourmanifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one... more

We show that the partition function of free Maxwell theory on a generic Euclidean fourmanifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one partition function of a 2d toroidal model, without the oscillator contributions. This map relates electric-magnetic duality t o modular invariance of the toroidal model and, conversely, the O(d; d 0 ; Z) duality to the invariance of Maxwell theory under the 4d mapping class group. These dualities and the relation between toroidal models and Maxwell theory can be understood by regarding both theories as dimensional reductions of a self-dual 2-form theory in six dimensions. Generalizations to more U(1)-gauge elds and reductions from higher dimensions are also discussed. We nd indications that the Abelian gauge theories related to 4d string theories with N = 4 space-time supersymmetry are exactly duality i n v ariant.

A wave equation on a one-dimensional interval I has a van der Pol type nonlinear boundary condition at the right end. At the left end, the boundary condition is fixed. At exactly the midpoint of the interval I, energy is injected into the... more

A wave equation on a one-dimensional interval I has a van der Pol type nonlinear boundary condition at the right end. At the left end, the boundary condition is fixed. At exactly the midpoint of the interval I, energy is injected into the system through a pair of transmission conditions in the feedback form of anti-damping. We wish to study chaotic wave propagation in the system. A cause of chaos by snapback repellers has been identified. These snapback repellers are repelling fixed points possessing homoclinic orbits of the non-invertible map in 2D corresponding to wave reflections and transmissions at, respectively, the boundary and the middleof-the-span points. Existing literature ͓F. R. Marotto, J. Math. Anal. Appl. 63, 199-223 ͑1978͔͒ on snapback repellers contains an error. We clarify the error and give a refined theorem that snapback repellers imply chaos. Numerical simulations of chaotic vibration are also illustrated.

We construct Bäcklund transformations (BTs) for the Kirchhoff top by taking advantage of the common algebraic Poisson structure between this system and the sl(2) trigonometric Gaudin model. Our BTs are integrable maps providing an exact... more

We construct Bäcklund transformations (BTs) for the Kirchhoff top by taking advantage of the common algebraic Poisson structure between this system and the sl(2) trigonometric Gaudin model. Our BTs are integrable maps providing an exact timediscretization of the system, inasmuch as they preserve both its Poisson structure and its invariants. Moreover, in some special cases we are able to show that these maps can be explicitly integrated in terms of the initial conditions and of the "iteration time" n. Encouraged by these partial results we make the conjecture that the maps are interpolated by a specific one-parameter family of hamiltonian flows, and present the corresponding solution. We enclose a few pictures where the orbits of the continuous and of the discrete flow are depicted.

The experimental consequences of neutrino mixing and decay are analyzed. Existing neutrino beam experiments are consistent with a finite but small mixing angle unless Im 2 -m2e t < (3.0 eV) 2. A finite v.. lifetime in the range r/my c 2 ~... more

The experimental consequences of neutrino mixing and decay are analyzed. Existing neutrino beam experiments are consistent with a finite but small mixing angle unless Im 2 -m2e t < (3.0 eV) 2. A finite v.. lifetime in the range r/my c 2 ~ 7 × 10 3 sec/MeV is shUown to be consistent with exper'~mental data. t~ Unified gauge theories in which the muon, the electron, and their neutrinos are combined into the same multiplet have interactions which violate separate muon and electron number conservation [la] **. Typically these interactions are suppressed by giving the appropriate gauge bosons a large mass. However, it is possible to have transitions between the two neutrinos which are not suppressed. Moreover, these theories also include right handed vector bosons which participate in self inter. actions that could generate a non-zero neutrino mass. The mixing of neutrino states and the radiative decay of the heavier neutrino are natural elements of such a unified gauge theory. For this reason it is desirable to examine the phenomenology of neutrino mixing and decay in order to determine the constraints imposed by existing experiments.

This paper proposes a Modular Universe toy-model (MUTM) predicting all elementary particles (EPs) to be actually quantum black-holes (QBHs) (gravitational quasi-singularities) governed by self-gravity and self-antigravity. This paper... more

This paper proposes a Modular Universe toy-model (MUTM) predicting all elementary particles (EPs) to be actually quantum black-holes (QBHs) (gravitational quasi-singularities) governed by self-gravity and self-antigravity. This paper continues (from an alternative angle of view) the work of other past articles/preprints of the same author in physics (cited in anti-chronological order, from the latest to the oldest.
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Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to... more

Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations. * Supported through the program Rientro dei Cervelli of the Italian Ministry of University and Research

The theoretical electronic densities of states for both the valence and conduction bands are presented for the tetrahedral semiconductors CdTe, HgTe and their alloy Hg 0:5 Cd0:5Te based on band structures computed using the empirical... more

The theoretical electronic densities of states for both the valence and conduction bands are presented for the tetrahedral semiconductors CdTe, HgTe and their alloy Hg 0:5 Cd0:5Te based on band structures computed using the empirical pseudopotential method. For the ternary alloy HgCdTe, we have coupled the virtual crystal approximation with the pseudopotential method. Various quantities such as the energy levels, the refractive index and the transverse e ective charge are calculated. The spin-orbit splitting is included in our calculations.

The splitting of separatrices for the standard-like maps F(x y) = y ;x + 2 y 1 + y 2 + "V 0 (y) = cosh h h > 0 " 2 R is measured. For even entire perturbative potentials V (y) = P n 2 V n y 2n such that b V (2 ) 6 = 0 , where b V ( ) = P... more

The splitting of separatrices for the standard-like maps F(x y) = y ;x + 2 y 1 + y 2 + "V 0 (y) = cosh h h > 0 " 2 R is measured. For even entire perturbative potentials V (y) = P n 2 V n y 2n such that b V (2 ) 6 = 0 , where b V ( ) = P n 2 V n 2n;1 =(2n ; 1)! is the Borel transform of V (y), the following asymptotic formula for the area A of the lobes between the perturbed separatrices is established

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the... more

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible (BFV) quantization of topological Yang-Mills theory are discussed. *

We characterize the dynamics of primitive molecular synthesis machines operating in outer space on quasi-one-dimensional channels where polymers interact with ÿxed particles. We show that a generic property of particle=polymer... more

We characterize the dynamics of primitive molecular synthesis machines operating in outer space on quasi-one-dimensional channels where polymers interact with ÿxed particles. We show that a generic property of particle=polymer electrostatic interactions is an average three monomer spacing between consecutive interaction potential minima. We exhibit that this property translates into locomotion regularities with a slowing down every three monomers. We argue that this transport property may be at the origin of the three base codon composition of the genetic code. We relate these ÿndings to present day protein synthesis mechanisms.

We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to... more

We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particles in the NUT spacetime.

Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic... more

Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Omegak0<0)(\Omega_{k_{0}}<0)(Omegak0<0) and for the Bianchi type-III (Omegak0>0)(\Omega_{k_{0}}>0)(Omegak0>0) with OmegaLambda0\Omega_{\Lambda_{0}}OmegaLambda0 smaller than some critical value OmegaLambdaM\Omega_{\Lambda_{M}}OmegaLambdaM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch ($z\approx 1000$), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if ∣Omega0+OmegaLambda0−1∣leqdelta|\Omega_0+\Omega_{\Lambda_0}-1|\leq \delta∣Omega0+OmegaLambda0−1∣leqdelta, for a very small delta\deltadelta . The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Omega0+OmegaLambda0=1\Omega_0+\Omega_{\Lambda_0}=1Omega0+OmegaLambda0=1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant OmegaLambda>OmegaLambdaM\Omega_\Lambda>\Omega_{\Lambda_{M}}OmegaLambda>OmegaLambdaM.

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Detrended fluctuation analysis (DFA) is used to investigate correlations between the monthly average of the maximum daily temperatures for different locations in the continental United States and the different climates these locations... more

Detrended fluctuation analysis (DFA) is used to investigate correlations between the monthly average of the maximum daily temperatures for different locations in the continental United States and the different climates these locations have. When we plot the scaling exponents obtained from the DFA versus the standard deviation of the temperature fluctuations, we observe crowding of data points belonging to the same climates. Thus, we conclude that by observing the long-time trends in the fluctuations of temperature it would be possible to distinguish between different climates.