scholarly journals Topological field theory approach to intermediate statistics

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Ward Vleeshouwers ◽  
Vladimir Gritsev
Keyword(s):  
Simons Theory ◽  
Unitary Matrix ◽  
Local Order ◽  
Theory Approach ◽  
Localization Transition ◽  
The Matrix ◽  
Random Matrix Models ◽  
Topological Field ◽  
Parameter Dependent ◽  
Physical Phenomena

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are characterized by the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szeg"{o}’s limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of U(N)U(N) Chern-Simons theory on S^3S3, and the SFF of this ensemble is proportional to the HOMFLY invariant of (2n,2)(2n,2)-torus links with one component in the fundamental and one in the antifundamental representation. This is one example of a large class of ensembles with intermediate statistics arising from topological field and string theories. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
Author(s):  
Samuel Monnier
Keyword(s):  
Topological Field Theories ◽  
Geometric Quantization ◽  
Discrete Symmetry ◽  
Local System ◽  
Field Theories ◽  
Simons Theory ◽  
General Point ◽  
Topological Field ◽  
Generalized Cohomology ◽  
Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

scholarly journals DNA Mutations via Chern–Simons Currents

2021 ◽  
Vol 136 (10) ◽  
Author(s):  
Francesco Bajardi ◽  
Lucia Altucci ◽  
Rosaria Benedetti ◽  
Salvatore Capozziello ◽  
Maria Rosaria Del Sorbo ◽  
...  
Keyword(s):  
Human Gene ◽  
Simons Theory ◽  
Topological Field Theory ◽  
Structure And Dynamics ◽  
Dna Mutations ◽  
Analogue Gravity ◽  
Topological Field ◽  
The Given ◽  
Chern Simons ◽  
Chern Simons Theory

AbstractWe test the validity of a possible schematization of DNA structure and dynamics based on the Chern–Simons theory, that is a topological field theory mostly considered in the context of effective gravity theories. By means of the expectation value of the Wilson Loop, derived from this analogue gravity approach, we find the point-like curvature of genomic strings in KRAS human gene and COVID-19 sequences, correlating this curvature with the genetic mutations. The point-like curvature profile, obtained by means of the Chern–Simons currents, can be used to infer the position of the given mutations within the genetic string. Generally, mutations take place in the highest Chern–Simons current gradient locations and subsequent mutated sequences appear to have a smoother curvature than the initial ones, in agreement with a free energy minimization argument.

Gaussian (N, z)-generalized Yang-Baxter operators

2016 ◽  
pp. 105-114
Author(s):  
Eric Rowell
Keyword(s):  
Bell States ◽  
Entangled States ◽  
Unitary Matrix ◽  
Baxter Equation ◽  
Careful Study ◽  
Standard Measurement ◽  
Measurement Basis ◽  
Parameter Dependent

We find unitary matrix solutions R˜(a) to the (multiplicative parameter-dependent) (N, z)-generalized Yang-Baxter equation that carry the standard measurement basis to m-level N-partite entangled states that generalize the 2-level bipartite entangled Bell states. This is achieved by a careful study of solutions to the Yang-Baxter equation discovered by Fateev and Zamolodchikov in 1982.

scholarly journals Exact results and Schur expansions in quiver Chern-Simons-matter theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Leonardo Santilli ◽  
Miguel Tierz
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Wilson Loops ◽  
Model Formulation ◽  
Schur Polynomials ◽  
Three Sphere ◽  
The Matrix ◽  
The Masses ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters tj = −e2πmj , where mj are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.

EXCITATIONS AND INTERACTIONS IN d=1 STRING THEORY

1991 ◽  
Vol 06 (11) ◽  
pp. 1961-1984 ◽  
Author(s):  
ANIRVAN M. SENGUPTA ◽  
SPENTA R. WADIA
Keyword(s):  
Matrix Model ◽  
Periodic Wave ◽  
Density Fluctuations ◽  
Dirac Fermion ◽  
Unitary Matrix ◽  
Additional Parameter ◽  
Continuum Approach ◽  
The Matrix ◽  
The One ◽  
The Continuum

We discuss the singlet sector of the d=1 matrix model in terms of a Dirac fermion formalism. The leading order two- and three-point functions of the density fluctuations are obtained by this method. This allows us to construct the effective action to that order and hence provide the equation of motion. This equation is compared with the one obtained from the continuum approach. We also compare continuum results for correlation functions with the matrix model ones and discuss the nature of gravitational dressing for this regularization. Finally, we address the question of boundary conditions within the framework of the d=1 unitary matrix model, considered as a regularized version of the Hermitian model, and study the implications of a generalized action with an additional parameter (analogous to the θ parameter) which give rise to quasi-periodic wave functions.

scholarly journals MATRIX MODELS WITHOUT SCALING LIMIT

1993 ◽  
Vol 08 (17) ◽  
pp. 2973-2992 ◽  
Author(s):  
L. BONORA ◽  
C. S. XIONG
Keyword(s):  
Matrix Models ◽  
Topological Field Theories ◽  
Continuum Limit ◽  
Scaling Limit ◽  
Exact Result ◽  
Field Theories ◽  
Kdv Hierarchy ◽  
The Matrix ◽  
Topological Field ◽  
Topological Gravity

In the context of Hermitian one-matrix models we show that the emergence of the NLS hierarchy and of its reduction, the KdV hierarchy, is an exact result of the lattice characterizing the matrix model. Said otherwise, we are not obliged to take a continuum limit to find these hierarchies. We interpret this result as an indication of the topological nature of them. We discuss the topological field theories associated with both and discuss the connection with topological field theories coupled to topological gravity already studied in the literature.

Exact elastic P/SV impedance

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. C7-C13 ◽  
Author(s):  
Igor B. Morozov
Keyword(s):  
Acoustic Impedance ◽  
Mode Conversion ◽  
Stress And Strain ◽  
S Wave ◽  
Impedance Inversion ◽  
The Matrix ◽  
Seismic Reflectivity ◽  
Parameter Dependent ◽  
Ray Parameter ◽  
Unambiguous Interpretation

Several extensions of the concept of acoustic impedance (AI) to oblique incidence exist and are known as elastic impedances (EI). These quantities are constructed by heuristic integrations of reflectivity series but still involve approximations and do not represent a unique medium property. Nevertheless, for unambiguous interpretation, it is desirable to have an EI that would (1) be a mechanical property of the medium and (2) yield exact reflection coefficients at all angles of incidence. Here, such a definition is given for P- and/or SV-wave propagation in an arbitrary isotropic medium. The exact elastic P/SV impedance is a matrix quantity and represents the differential operator relating the stress and strain boundary conditions. With the use of the matrix form of the reflectivity problem, no approximations are required for accurate modeling of reflection (P/P and SV/SV) and mode-conversion (P/SV and SV/P) coefficients at all angles and for any contrasts in elastic properties. The matrix EI can be computed from real well logs and inverted from ray-parameter-dependent seismic reflectivity. Known limiting cases of P- and S-wave acoustic impedances are accurately reproduced and the approach also allows the extension of the concept of impedance to an attenuative medium. The matrix impedance readily lends itself to inversion with uncertainties typical of the standard acoustic-impedance inversion problem.

scholarly journals A limit distribution for a quantum walk driven by a five-diagonal unitary matrix

2021 ◽  
Vol 21 (1&2) ◽  
pp. 0019-0036
Author(s):  
Takuya Machida
Keyword(s):  
Time Evolution ◽  
Limit Distribution ◽  
Quantum Walk ◽  
Time Limit ◽  
Unitary Matrix ◽  
Exact Form ◽  
Special Values ◽  
The Matrix ◽  
Long Time ◽  
Phase Term

In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a location and delocalizes in distribution as its system is getting updated. The five-diagonal matrix contains a phase term and the quantum walk becomes a standard coined walk when the phase term is fixed at special values. Or, the phase term gives an effect on the quantum walk. As a result, we will see an explicit form of a long-time limit distribution for a quantum walk driven by the matrix, and thanks to the exact form, we understand how the quantum walker approximately distributes in space after the long-time evolution has been executed on the walk.

scholarly journals Dynamical Invariant Applied on General Time-Dependent Three Coupled Nano-Optomechanical Oscillators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sara Hassoul ◽  
Salah Menouar ◽  
Hamid Benseridi ◽  
Jeong Ryeol Choi
Keyword(s):  
Invariant Operator ◽  
Time Dependent ◽  
Unitary Matrix ◽  
Optomechanical System ◽  
Von Neumann ◽  
Classical Counterpart ◽  
Quadratic Invariant ◽  
Fock State ◽  
The Matrix ◽  
General Time

A quadratic invariant operator for general time-dependent three coupled nano-optomechanical oscillators is investigated. We show that the invariant operator that we have established satisfies the Liouville-von Neumann equation and coincides with its classical counterpart. To diagonalize the invariant, we carry out a unitary transformation of it at first. From such a transformation, the quantal invariant operator reduces to an equal, but a simple one which corresponds to three coupled oscillators with time-dependent frequencies and unit masses. Finally, we diagonalize the matrix representation of the transformed invariant by using a unitary matrix. The diagonalized invariant is just the same as the Hamiltonian of three simple oscillators. Thanks to such a diagonalization, we can analyze various dynamical properties of the nano-optomechanical system. Quantum characteristics of the system are investigated as an example, by utilizing the diagonalized invariant. We derive not only the eigenfunctions of the invariant operator, but also the wave functions in the Fock state.

scholarly journals CONSTRAINTS ON MASS MATRICES DUE TO MEASURED PROPERTY OF THE MIXING MATRIX

2006 ◽  
Vol 21 (11) ◽  
pp. 907-910 ◽  
Author(s):  
S. CHATURVEDI ◽  
VIRENDRA GUPTA
Keyword(s):  
Hermitian Matrix ◽  
Main Diagonal ◽  
Unitary Matrix ◽  
Matrix Elements ◽  
Mass Matrices ◽  
The Matrix ◽  
Measured Property ◽  
Mixing Matrix ◽  
The Asymmetry

It is shown that two specific properties of the unitary matrix V can be expressed directly in terms of the matrix elements and eigenvalues of the hermitian matrix M which is diagonalized by V. These are the asymmetry Δ(V) = |V12|2-|V21|2, of V with respect to the main diagonal and the Jarlskog invariant [Formula: see text]. These expressions for Δ(V) and J(V) provide constraints on possible mass matrices from the available data on V.

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