Holographic fermions at strong translational symmetry breaking: a Bianchi-VII case study

It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion response computed by the emergent quantum critical IR, even when the potential becomes relevant in the infra-red. However, in the regime where holographic quasi-particles occur, defining a Fermi surface in the continuum, they acquire a finite lifetime at any finite potential strength. At the transition from irrelevancy to relevancy of the Bianchi potential in the deep infra-red the quasi-particle remnants disappear completely and the fermion spectrum exhibits a purely relaxational behaviour.Comment: 30 pages, 10 figure

On the exact Foldy-Wouthuysen transformation for a Dirac spinor in torsion and other CPT and Lorentz violating backgrounds

We discuss the possibility to perform and use the exact Foldy-Wouthuysen transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz violating terms. The classification of such terms is performed, selecting those of them which admit EFWT. For the particular example of an axial vector field, which can be associated with the completely antisymmetric torsion, we construct an explicit EFWT in the case when only a timelike component of this axial vector is present. In the cases when EFWT is not possible, one can still use the corresponding technique for deriving the perturbative Foldy-Wouthuysen transformation, as is illustrated in a particular example in the Appendix

FACE RECOGNITION WITH LOW FALSE POSITIVE ERROR RATE

Nowadays face recognition systems are widely used in the world. In China these systems are used in safe cities projects in production, in Russia they are used mostly in closed-loop systems like factories, business centers with biometric access control or stadiums. Closed loop means that we need to identify people from a fixed dataset: in factory it’s a list of employees, in stadium it’s a list of ticket owners. The most challenging task is to identify people from some large city with an open dataset: we don’t have a fixed set of people in the city, it’s rapidly changing due to migration. Another limit is the accuracy of the system: we can’t make a lot of false positive errors (when a person is incorrectly recognized as another person) because number of human operators is limited and they are expensive. We propose an approach to maximize face recognition accuracy for a fixed false positive error rate using limited amount of hardware

Quantum deformation of the angular distributions of synchrotron radiation. Emission of particles in the first excited state

The exact expressions for the characteristics of synchrotron radiation of charged particles in the first excited state are obtained in analytical form using quantum theory methods. We performed a detailed analysis of the angular distribution structure of radiation power and its polarization for particles with spin 0 and 1/2. It is shown that the exact quantum calculations lead to results that differ substantially from the predictions of classical theory

Generalization properties of neural network approximations to frustrated magnet ground states

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility

Generalization properties of neural network approximations to frustrated magnet ground states

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility. © 2020, The Author(s).Russian Science Foundation, RSF: 18-12-00185, 16-12-10059Alexander von Humboldt-Stiftung: 0033-2019-0002Nederlandse Organisatie voor Wetenschappelijk Onderzoek, NWOEuropean Research Council, ERC: 338957 FEMTO/ NANOWe are thankful to Dmitry Ageev and Vladimir Mazurenko for collaboration during the early stages of the project. We have significantly benefited from encouraging discussions with Giuseppe Carleo, Juan Carrasquilla, Askar Iliasov, Titus Neupert, and Slava Rychkov. The research was supported by the ERC Advanced Grant 338957 FEMTO/ NANO and by the NWO via the Spinoza Prize. The work of A.A.B. which consisted of designing the project (together with K.S.T.), implementation of prototype version of the code, and providing general guidance, was supported by Russian Science Foundation, Grant no. 18-12-00185. The work of N.A. which consisted of numerical experiments, was supported by the Russian Science Foundation Grant no. 16-12-10059. N.A. acknowledges the use of computing resources of the federal collective usage center Complex for Simulation and Data Processing for Mega-science Facilities at NRC "Kurchatov Institute”, http://ckp.nrcki.ru/. K.S.T. is supported by Alexander von Humboldt Foundation and by the program 0033-2019-0002 by the Ministry of Science and Higher Education of Russia

Dirac fermions in strong electric field and quantum transport in graphene

Our previous results on the nonperturbative calculations of the mean current and of the energy-momentum tensor in QED with the T-constant electric field are generalized to arbitrary dimensions. The renormalized mean values are found; the vacuum polarization and particle creation contributions to these mean values are isolated in the large T-limit, the vacuum polarization contributions being related to the one-loop effective Euler-Heisenberg Lagrangian. Peculiarities in odd dimensions are considered in detail. We adapt general results obtained in 2+1 dimensions to the conditions which are realized in the Dirac model for graphene. We study the quantum electronic and energy transport in the graphene at low carrier density and low temperatures when quantum interference effects are important. Our description of the quantum transport in the graphene is based on the so-called generalized Furry picture in QED where the strong external field is taken into account nonperturbatively; this approach is not restricted to a semiclassical approximation for carriers and does not use any statistical assumtions inherent in the Boltzmann transport theory. In addition, we consider the evolution of the mean electromagnetic field in the graphene, taking into account the backreaction of the matter field to the applied external field. We find solutions of the corresponding Dirac-Maxwell set of equations and with their help we calculate the effective mean electromagnetic field and effective mean values of the current and the energy-momentum tensor. The nonlinear and linear I-V characteristics experimentally observed in both low and high mobility graphene samples is quite well explained in the framework of the proposed approach, their peculiarities being essentially due to the carrier creation from the vacuum by the applied electric field.Comment: 24 pages, 1 figure; version accepted for publication in Physical Review D., some comments adde

Radiative polarization of electrons in a strong laser wave

We reanalyze the problem of radiative polarization of electrons brought into collision with a circularly polarized strong plane wave. We present an independent analytical verification of formulae for the cross section given by D.\,Yu. Ivanov et al [Eur.\ Phys.\ J. C \textbf{36}, 127 (2004)]. By choosing the exact electron's helicity as the spin quantum number we show that the self-polarization effect exists only for the moderately relativistic electrons with energy $\gamma = E/mc^2 \lesssim 10$ and only for a non-head-on collision geometry. In these conditions polarization degree may achieve the values up to 65%, but the effective polarization time is found to be larger than 1\,s even for a high power optical or infrared laser with intensity parameter $\xi = |{\bf E}| m c^2/E_c \hbar \omega \sim 0.1$ ($E_c = m^2 c^3/e \hbar$). This makes such a polarization practically unrealizable. We also compare these results with the ones of some papers where the high degree of polarization was predicted for ultrarelativistic case. We argue that this apparent contradiction arises due to the different choice of the spin quantum numbers. In particular, the quantum numbers which provide the high polarization degree represent neither helicity nor transverse polarization, that makes the use of them inconvenient in practice.Comment: minor changes compared to v3; to appear in PR