scholarly journals Chaos on the hypercube

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yiyang Jia ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Magnetic Flux ◽  
Spectral Density ◽  
Hermite Polynomials ◽  
Weighted Sums ◽  
Majorana Fermions ◽  
Chord Diagrams ◽  
Magnetic Inversion ◽  
Constant Magnitude ◽  
Kitaev Model ◽  
Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

scholarly journals Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 541 ◽  
Author(s):  
Venkata Kota ◽  
Narendra Chavda
Keyword(s):  
Hermite Polynomials ◽  
Point Group ◽  
Majorana Fermions ◽  
Many Body ◽  
Boson Systems ◽  
Random Matrix Ensembles ◽  
Isolated Systems ◽  
Group Symmetries ◽  
Statistical Relaxation

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

scholarly journals Role of Majorana fermions in spin transport of anisotropic Kitaev model

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
Hirokazu Taguchi ◽  
Yuta Murakami ◽  
Akihisa Koga ◽  
Joji Nasu
Keyword(s):  
Spin Transport ◽  
Majorana Fermions ◽  
Kitaev Model

scholarly journals The Re-examination of Adjustment of the Rotor Magnetic Field Observer in the Induction Motor

2013 ◽  
Vol 4 (1) ◽  
pp. 38-44
Author(s):  
Alexander Burkov ◽  
Evgenii Krasilnikyants ◽  
Alexander Smirnov ◽  
Georgy Bouldukan
Keyword(s):  
Magnetic Flux ◽  
Induction Motor ◽  
Induction Motors ◽  
Motor Drives ◽  
Fine Tuning ◽  
Active Components ◽  
Induction Motor Drives ◽  
Flux Observer ◽  
Stator Current ◽  
Constant Magnitude

Abstract Wide use of induction motor drives makes the problems related to induction motors very topical. One of such problems is the maximal utilization of torque and velocity of induction motors. In this regard the use and accurate adjustment of rotor magnetic flux observers may be helpful. The technique of observer adjustment is subject of special interest. This technique can be regarded as optimal if it ensures constant acceleration that, in turn, corresponds to constant magnitude of active and magnetizing components of stator current. In contrast, nonoptimal tuning of the magnetic flux observer creates a transient response caused by variation of magnetic and active components of the stator current resulting in changing acceleration of the motor. However, the parameters of non-optimal process can be used for fine tuning of the observer which considers the variation of the time constants obtained analyzing the drive's magnetic circuit saturation. It is possible to conclude that implementation of fine adjustment of rotor magnetic flux observer is of critical importance for induction motor torque and velocity maximum utilization.

scholarly journals AN AUTOREGRESSIVE SPECTRAL DENSITY ESTIMATOR AT FREQUENCY ZERO FOR NONSTATIONARITY TESTS

1998 ◽  
Vol 14 (5) ◽  
pp. 560-603 ◽  
Author(s):  
Pierre Perron ◽  
Serena Ng
Keyword(s):  
Spectral Density ◽  
Serial Correlation ◽  
Mean Squared Error ◽  
Spectral Density Function ◽  
Weighted Sums ◽  
Density Estimator ◽  
Correlated Errors ◽  
Squared Error ◽  
Cointegration Tests ◽  
Asymptotic Analyses

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant increase in the bias and mean-squared error (MSE) of kernel-based estimators. We then consider a variant of the autoregressive spectral density estimator that does not share these shortcomings because it bypasses the use of the estimate from the AR(1) regression. Simulations and local asymptotic analyses show its bias and MSE to be much smaller than those of a kernel-based estimator when there is strong negative serial correlation. We also include a discussion about the appropriate choice of the truncation lag.

scholarly journals Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N

2017 ◽  
Vol 96 (6) ◽  
Author(s):  
Antonio M. García-García ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Spectral Density ◽  
Kitaev Model

scholarly journals Q -Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model

2022 ◽  
Vol 105 (2) ◽  
Author(s):  
Lucas Sá ◽  
Antonio M. García-García
Keyword(s):  
Spectral Density ◽  
Quantum Chaos ◽  
Kitaev Model

scholarly journals Anderson–Kitaev spin liquid

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Masahiko G. Yamada
Keyword(s):  
Time Reversal ◽  
Hall Current ◽  
Quantum Hall ◽  
Spin Liquid ◽  
Majorana Fermions ◽  
Disorder Strength ◽  
Spin Liquids ◽  
Kitaev Model ◽  
Mass Terms ◽  
The Stability

Abstract The bond-disordered Kitaev model attracts much attention due to the experimental relevance in α-RuCl3 and A3LiIr2O6 (A = H, D, Ag, etc.). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions. The quantization of the thermal Hall conductivity κxy/T disappears by a quantum Hall transition induced by a small disorder, and κxy/T shows a rapid crossover into a state with a negligible Hall current. We call this immobile liquid state Anderson–Kitaev spin liquid (AKSL). Especially, the critical disorder strength δJc1 ~ 0.05 in the unit of the Kitaev interaction would have many implications for the stability of Kitaev spin liquids.

Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

2000 ◽  
Vol 179 ◽  
pp. 263-264
Author(s):  
K. Sundara Raman ◽  
K. B. Ramesh ◽  
R. Selvendran ◽  
P. S. M. Aleem ◽  
K. M. Hiremath
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Ultra Violet ◽  
Active Regions ◽  
Morphological Properties ◽  
Energy Storage And Conversion ◽  
The Sun ◽  
X Rays ◽  
The Magnetic Field

Extended AbstractWe have examined the morphological properties of a sigmoid associated with an SXR (soft X-ray) flare. The sigmoid is cospatial with the EUV (extreme ultra violet) images and in the optical part lies along an S-shaped Hαfilament. The photoheliogram shows flux emergence within an existingδtype sunspot which has caused the rotation of the umbrae giving rise to the sigmoidal brightening.It is now widely accepted that flares derive their energy from the magnetic fields of the active regions and coronal levels are considered to be the flare sites. But still a satisfactory understanding of the flare processes has not been achieved because of the difficulties encountered to predict and estimate the probability of flare eruptions. The convection flows and vortices below the photosphere transport and concentrate magnetic field, which subsequently appear as active regions in the photosphere (Rust & Kumar 1994 and the references therein). Successive emergence of magnetic flux, twist the field, creating flare productive magnetic shear and has been studied by many authors (Sundara Ramanet al.1998 and the references therein). Hence, it is considered that the flare is powered by the energy stored in the twisted magnetic flux tubes (Kurokawa 1996 and the references therein). Rust & Kumar (1996) named the S-shaped bright coronal loops that appear in soft X-rays as ‘Sigmoids’ and concluded that this S-shaped distortion is due to the twist developed in the magnetic field lines. These transient sigmoidal features tell a great deal about unstable coronal magnetic fields, as these regions are more likely to be eruptive (Canfieldet al.1999). As the magnetic fields of the active regions are deep rooted in the Sun, the twist developed in the subphotospheric flux tube penetrates the photosphere and extends in to the corona. Thus, it is essentially favourable for the subphotospheric twist to unwind the twist and transmit it through the photosphere to the corona. Therefore, it becomes essential to make complete observational descriptions of a flare from the magnetic field changes that are taking place in different atmospheric levels of the Sun, to pin down the energy storage and conversion process that trigger the flare phenomena.

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