51 research outputs found
Secularly growing loop corrections in strong electric fields
We calculate one--loop corrections to the vertexes and propagators of photons
and charged particles in the strong electric field backgrounds. We use the
Schwinger--Keldysh diagrammatic technique. We observe that photon's Keldysh
propagator receives growing with time infrared contribution. As the result,
loop corrections are not suppressed in comparison with tree--level
contribution. This effect substantially changes the standard picture of the
pair production. To sum up leading IR corrections from all loops we consider
the infrared limit of the Dyson--Schwinger equations and reduce them to a
single kinetic equation.Comment: 16 pages, no figures; Minor correction
Many-body effects in graphene beyond the Dirac model with Coulomb interaction
This paper is devoted to development of perturbation theory for studying the
properties of graphene sheet of finite size, at nonzero temperature and
chemical potential. The perturbation theory is based on the tight-binding
Hamiltonian and arbitrary interaction potential between electrons, which is
considered as a perturbation. One-loop corrections to the electron propagator
and to the interaction potential at nonzero temperature and chemical potential
are calculated. One-loop formulas for the energy spectrum of electrons in
graphene, for the renormalized Fermi velocity and also for the dielectric
permittivity are derived.Comment: 11 pages, 11 figure
Study of shear viscosity of SU (2)-gluodynamics within lattice simulation
This paper is devoted to the study of two-point correlation function of the
energy-momentum tensor T_{12}T_{12} for SU(2)-gluodynamics within lattice
simulation of QCD. Using multilevel algorithm we carried out the measurement of
the correlation function at the temperature T/T_c = 1.2. It is shown that
lattice data can be described by spectral functions which interpolate between
hydrodynamics at low frequencies and asymptotic freedom at high frequencies.
The results of the study of spectral functions allowed us to estimate the ratio
of shear viscosity to the entropy density {\eta}/s = 0.134 +- 0.057.Comment: 7 pages, 3 figure
Quantum Monte Carlo study of static potential in graphene
In this paper the interaction potential between static charges in suspended
graphene is studied within the quantum Monte Carlo approach. We calculated the
dielectric permittivity of suspended graphene for the set of temperatures and
extrapolated our results to zero temperature. The dielectric permittivity at
zero temperature has the following properties. At zero distance
. Then it rises and at a large distance the dielectric
permittivity reaches the plateau . The results
obtained in this paper allow to draw a conclusion that full account of
many-body effects in the dielectric permittivity of suspended graphene gives
very close to the one-loop results. Contrary to the one-loop result,
the two-loop prediction for the dielectric permittivity deviates from our
result. So, one can expect large higher order corrections to the two-loop
prediction for the dielectric permittivity of suspended graphene.Comment: 6 pages, 2 figure
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
NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code
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