Alexander Molochkov - Academia.edu (original) (raw)

Papers by Alexander Molochkov

Physical Review D

Compact U(1) gauge theory in 3+1 dimensions possesses the confining phase, characterized by a lin... more Compact U(1) gauge theory in 3+1 dimensions possesses the confining phase, characterized by a linear raise of the potential between particles with opposite electric charges at sufficiently large inter-particle separation. The confinement is generated by condensation of Abelian monopoles at strong gauge coupling. We study the properties of monopoles and deconfining order parameter in zero-temperature theory in the presence of ideally conducting parallel metallic boundaries (plates) usually associated with the Casimir effect. Using first-principle numerical simulations in compact U(1) lattice gauge theory, we show that as the distance between the plates diminishes, the vacuum in between the plates experiences a deconfining transition. The phase diagram in the space of the gauge coupling and the inter-plane distance is obtained.

SciPost Physics Proceedings

We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge th... more We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.

AIP Conference Proceedings, 2011

ABSTRACT The deep inelastic scattering of leptons off nuclei is studied within the the Bethe-Salp... more ABSTRACT The deep inelastic scattering of leptons off nuclei is studied within the the Bethe-Salpeter formalism. It is shown that nuclear short-range structure can be expressed in terms of the nucleon structure functions and four-dimensional Fermi motion of the nucleons. The four-dimensional Fermi motion broadens the bound nucleon localization area, what leads to the observation of the nucleon structure change in nuclei--EMC effect. The 4He to deuteron structure functions ratio is found in good agreement with experimental data. It is shown that the pattern of the ratio is defined by dynamical properties of the nucleon structure and four-dimensional geometry of the bound state.

Physical Review Letters

Using first-principle lattice simulations, we demonstrate that in the background of a strong magn... more Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10 20 T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum. We find evidence that the vortices form a disordered solid or a liquid rather than a crystal. The second transition restores the electroweak symmetry. Such conditions can be realized in the near-horizon region of the magnetized black holes.

PLOS ONE, Jan 13, 2021

We investigate aspects of topology in protein folding. For this we numerically simulate the tempe... more We investigate aspects of topology in protein folding. For this we numerically simulate the temperature driven folding and unfolding of the slipknotted archaeal virus protein AFV3-109. Due to knottiness the (un)folding is a topological process, it engages the entire backbone in a collective fashion. Accordingly we introduce a topological approach to model the process. Our simulations reveal that the (un)folding of AFV3-109 slipknot proceeds through a folding intermediate that has the topology of a trefoil knot. We observe that the final slipknot causes a slight swelling of the folded AFV3-109 structure. We disclose the relative stability of the strands and helices during both the folding and unfolding processes. We confirm results from previous studies that pointed out that it can be very demanding to simulate the formation of knotty self-entanglement, and we explain how the problems are circumvented: The slipknotted AFV3-109 protein is a very slow folder with a topologically demanding pathway, which needs to be properly accounted for in a simulation description. When we either increase the relative stiffness of bending, or when we decrease the speed of ambient cooling, the rate of slipknot formation rapidly increases.

EPJ Web of Conferences, 2018

Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase t... more Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions Z n (T) are coefficients of this expansion. Using various methods we study properties of Z n (T). At the last step we perform cubic spline for temperature dependence of Z n (T) at fixed n and compute baryon number susceptibility χ B /T 2 as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 16 3 × 4 lattice with m π /m ρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line T c (µ 2 B) = T c c − κ µ 2 B /T 2 c with κ = −0.0453 ± 0.0099.

Physics Letters B, 2019

Quantum polarization effects associated with the conformal anomaly in a static magnetic field bac... more Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum. The current may be produced either in an unbounded curved spacetime or in a flat spacetime in a physically bounded system. In both cases, the magnitude of the electric current is proportional to the beta-function associated with renormalization of the electric charge. In our article, we investigate the electric current density induced by the magnetic field in the vicinity of a Dirichlet boundary in the scalar QED. Using first-principle lattice simulations we show that the electric current, generated by this "conformal magnetic effect at the edge" (CMEE), is well described by the conformal anomaly provided the conformal symmetry is classically unbroken. Outside of the conformal limit, the current density is characterized by an anomalous power law near the edge of the system and by an exponential suppression of the current far away from the edge.

Physics Letters B, 1999

The evolution of the nucleon structure as a function of atomic mass A is considered for the first... more The evolution of the nucleon structure as a function of atomic mass A is considered for the first time for the lightest nuclei, D, 3 H, 3 He and 4 He, with an approach based on the Bethe-Salpeter formalism. We show that the pattern of the oscillation of the structure functions ratio r A (x) = F A 2 /F N(D) 2 varies with A by changing the position of the crossover point x 3 in which r A (x) = 1, unlike the pattern for nuclei with masses A > 4, where only the amplitude of the oscillation changes. In particular we find that the pattern of F 2 (x) modifications is controlled with the values (1 − x 3) = 0.32 (D/N), 0.16 (3 He/D) and 0.08 (4 He/D). The obtained results follow from the relativistic consideration of the nuclear structure and allow us to define a whole class of modifications of the partonic distributions in the nucleon bound in a nucleus. The EMC effect is explained as a particular case of the considered class.

Cornell University - arXiv, Aug 6, 2022

The review of vacuum and matter restructuring in space-time with boundaries is presented. We cons... more The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates. We also discuss mass scale shifts in such systems and their possible dynamical and geometrical nature.

Cornell University - arXiv, Jul 28, 2019

We propose new way of heavy ion collisions experiment data analysis. We analyze physical paramete... more We propose new way of heavy ion collisions experiment data analysis. We analyze physical parameters of fireball created in RHIC experiment based on Grand Canonical Distribution and different Lattice QCD data available at the moment. Our results on chemical potential are in agreement with previous model estimations and do not depend on Lattice setup. At same time, we found possible T(V) states of fireball and estimated the most probable temperature and volume of fireball as function of collision energy. We conclude that hadrom matter at RHIC experiment is thermalized and described by Grand Canonical Distribution.

Le Centre pour la Communication Scientifique Directe - HAL - Université Francois Rabelais - Tours, Aug 2, 2021

We discuss the properties of the non-Hermitian PT-symmetric twoscalar fields model. We investigat... more We discuss the properties of the non-Hermitian PT-symmetric twoscalar fields model. We investigate stability areas of this system and properties of vortices that emerge in the system of two interacting scalar fields. The phase diagram of the model contains stable and unstable regions depending on PT-symmetry breaking, which intercross the regions of U(1)-symmetric and U(1)-broken phases in a nontrivial way. At non-zero quartic couplings, the non-Hermitian model possesses classical vortex solutions in the PT-symmetric regions. We also consider a close Hermitian analog of the theory and compare the results with the non-Hermitian model.

Physical Review Research, 2020

Progress of Theoretical and Experimental Physics, 2017

The canonical approach, which was developed for solving the sign problem, may suffer from a new t... more The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In this method, the grand partition function is written as a fugacity expansion: Z G (μ, T) = n Z C (n, T)ξ n , where ξ = exp(μ/T) is the fugacity, and Z C (n, T) are given as averages over a Monte Carlo update, z n. We show that the complex phase of z n is proportional to n at each Monte Carlo step. Although z n take real positive values, the values of z n fluctuate rapidly when n is large, especially in the confinement phase, which gives a limit on n.

Physical Review D, 2021

We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-timesy... more We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-timesymmetric relativistic model possessing two interacting scalar complex fields. The phase diagram contains stable PT-symmetric regions and unstable PT-broken regions, which intertwine nontrivially with the U(1)-symmetric and U(1)-broken phases, thus forming rich patterns in the space of parameters of the model. The notion of the PT symmetry breaking is generalized to the interacting theory. At finite quartic couplings, the non-Hermitian model possesses classical vortex solutions in the PT-symmetric regions characterized by broken U(1) symmetry. In the long-range limit of twocomponent Bose-Einstein condensates, the vortices from different condensates experience mutual dissipative dynamics unless their cores overlap precisely. For comparison, we also consider a close Hermitian analog of the system and demonstrate that the non-Hermitian two-component model possesses much richer dynamics than its Hermitian counterpart.

The Journal of Physical Chemistry B

EPJ Web of Conferences, 2018

We simulate lattice QCD with two flavors of Wilson fermions at imaginary baryon chemical potentia... more We simulate lattice QCD with two flavors of Wilson fermions at imaginary baryon chemical potential. Results for the baryon number density computed in the confining and deconfining phases at imaginary baryon chemical potential are used to determine the baryon number density and higher cumulants at the real chemical potential via analytical continuation.

Physical Review Letters, 2018

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principl... more We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principle numerical simulations. Working in two spatial dimensions at zero temperature we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.

Physical Review Letters, 2018

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principl... more We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principle numerical simulations. Working in two spatial dimensions at zero temperature we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.

Physical Review D

Compact U(1) gauge theory in 3+1 dimensions possesses the confining phase, characterized by a lin... more Compact U(1) gauge theory in 3+1 dimensions possesses the confining phase, characterized by a linear raise of the potential between particles with opposite electric charges at sufficiently large inter-particle separation. The confinement is generated by condensation of Abelian monopoles at strong gauge coupling. We study the properties of monopoles and deconfining order parameter in zero-temperature theory in the presence of ideally conducting parallel metallic boundaries (plates) usually associated with the Casimir effect. Using first-principle numerical simulations in compact U(1) lattice gauge theory, we show that as the distance between the plates diminishes, the vacuum in between the plates experiences a deconfining transition. The phase diagram in the space of the gauge coupling and the inter-plane distance is obtained.

SciPost Physics Proceedings

We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge th... more We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.

AIP Conference Proceedings, 2011

ABSTRACT The deep inelastic scattering of leptons off nuclei is studied within the the Bethe-Salp... more ABSTRACT The deep inelastic scattering of leptons off nuclei is studied within the the Bethe-Salpeter formalism. It is shown that nuclear short-range structure can be expressed in terms of the nucleon structure functions and four-dimensional Fermi motion of the nucleons. The four-dimensional Fermi motion broadens the bound nucleon localization area, what leads to the observation of the nucleon structure change in nuclei--EMC effect. The 4He to deuteron structure functions ratio is found in good agreement with experimental data. It is shown that the pattern of the ratio is defined by dynamical properties of the nucleon structure and four-dimensional geometry of the bound state.

Physical Review Letters

Using first-principle lattice simulations, we demonstrate that in the background of a strong magn... more Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10 20 T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum. We find evidence that the vortices form a disordered solid or a liquid rather than a crystal. The second transition restores the electroweak symmetry. Such conditions can be realized in the near-horizon region of the magnetized black holes.

PLOS ONE, Jan 13, 2021

We investigate aspects of topology in protein folding. For this we numerically simulate the tempe... more We investigate aspects of topology in protein folding. For this we numerically simulate the temperature driven folding and unfolding of the slipknotted archaeal virus protein AFV3-109. Due to knottiness the (un)folding is a topological process, it engages the entire backbone in a collective fashion. Accordingly we introduce a topological approach to model the process. Our simulations reveal that the (un)folding of AFV3-109 slipknot proceeds through a folding intermediate that has the topology of a trefoil knot. We observe that the final slipknot causes a slight swelling of the folded AFV3-109 structure. We disclose the relative stability of the strands and helices during both the folding and unfolding processes. We confirm results from previous studies that pointed out that it can be very demanding to simulate the formation of knotty self-entanglement, and we explain how the problems are circumvented: The slipknotted AFV3-109 protein is a very slow folder with a topologically demanding pathway, which needs to be properly accounted for in a simulation description. When we either increase the relative stiffness of bending, or when we decrease the speed of ambient cooling, the rate of slipknot formation rapidly increases.

EPJ Web of Conferences, 2018

Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase t... more Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions Z n (T) are coefficients of this expansion. Using various methods we study properties of Z n (T). At the last step we perform cubic spline for temperature dependence of Z n (T) at fixed n and compute baryon number susceptibility χ B /T 2 as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 16 3 × 4 lattice with m π /m ρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line T c (µ 2 B) = T c c − κ µ 2 B /T 2 c with κ = −0.0453 ± 0.0099.

Physics Letters B, 2019

Quantum polarization effects associated with the conformal anomaly in a static magnetic field bac... more Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum. The current may be produced either in an unbounded curved spacetime or in a flat spacetime in a physically bounded system. In both cases, the magnitude of the electric current is proportional to the beta-function associated with renormalization of the electric charge. In our article, we investigate the electric current density induced by the magnetic field in the vicinity of a Dirichlet boundary in the scalar QED. Using first-principle lattice simulations we show that the electric current, generated by this "conformal magnetic effect at the edge" (CMEE), is well described by the conformal anomaly provided the conformal symmetry is classically unbroken. Outside of the conformal limit, the current density is characterized by an anomalous power law near the edge of the system and by an exponential suppression of the current far away from the edge.

Physics Letters B, 1999

The evolution of the nucleon structure as a function of atomic mass A is considered for the first... more The evolution of the nucleon structure as a function of atomic mass A is considered for the first time for the lightest nuclei, D, 3 H, 3 He and 4 He, with an approach based on the Bethe-Salpeter formalism. We show that the pattern of the oscillation of the structure functions ratio r A (x) = F A 2 /F N(D) 2 varies with A by changing the position of the crossover point x 3 in which r A (x) = 1, unlike the pattern for nuclei with masses A > 4, where only the amplitude of the oscillation changes. In particular we find that the pattern of F 2 (x) modifications is controlled with the values (1 − x 3) = 0.32 (D/N), 0.16 (3 He/D) and 0.08 (4 He/D). The obtained results follow from the relativistic consideration of the nuclear structure and allow us to define a whole class of modifications of the partonic distributions in the nucleon bound in a nucleus. The EMC effect is explained as a particular case of the considered class.

Cornell University - arXiv, Aug 6, 2022

The review of vacuum and matter restructuring in space-time with boundaries is presented. We cons... more The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates. We also discuss mass scale shifts in such systems and their possible dynamical and geometrical nature.

Cornell University - arXiv, Jul 28, 2019

We propose new way of heavy ion collisions experiment data analysis. We analyze physical paramete... more We propose new way of heavy ion collisions experiment data analysis. We analyze physical parameters of fireball created in RHIC experiment based on Grand Canonical Distribution and different Lattice QCD data available at the moment. Our results on chemical potential are in agreement with previous model estimations and do not depend on Lattice setup. At same time, we found possible T(V) states of fireball and estimated the most probable temperature and volume of fireball as function of collision energy. We conclude that hadrom matter at RHIC experiment is thermalized and described by Grand Canonical Distribution.

Le Centre pour la Communication Scientifique Directe - HAL - Université Francois Rabelais - Tours, Aug 2, 2021

We discuss the properties of the non-Hermitian PT-symmetric twoscalar fields model. We investigat... more We discuss the properties of the non-Hermitian PT-symmetric twoscalar fields model. We investigate stability areas of this system and properties of vortices that emerge in the system of two interacting scalar fields. The phase diagram of the model contains stable and unstable regions depending on PT-symmetry breaking, which intercross the regions of U(1)-symmetric and U(1)-broken phases in a nontrivial way. At non-zero quartic couplings, the non-Hermitian model possesses classical vortex solutions in the PT-symmetric regions. We also consider a close Hermitian analog of the theory and compare the results with the non-Hermitian model.

Physical Review Research, 2020

Progress of Theoretical and Experimental Physics, 2017

The canonical approach, which was developed for solving the sign problem, may suffer from a new t... more The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In this method, the grand partition function is written as a fugacity expansion: Z G (μ, T) = n Z C (n, T)ξ n , where ξ = exp(μ/T) is the fugacity, and Z C (n, T) are given as averages over a Monte Carlo update, z n. We show that the complex phase of z n is proportional to n at each Monte Carlo step. Although z n take real positive values, the values of z n fluctuate rapidly when n is large, especially in the confinement phase, which gives a limit on n.

Physical Review D, 2021

We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-timesy... more We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-timesymmetric relativistic model possessing two interacting scalar complex fields. The phase diagram contains stable PT-symmetric regions and unstable PT-broken regions, which intertwine nontrivially with the U(1)-symmetric and U(1)-broken phases, thus forming rich patterns in the space of parameters of the model. The notion of the PT symmetry breaking is generalized to the interacting theory. At finite quartic couplings, the non-Hermitian model possesses classical vortex solutions in the PT-symmetric regions characterized by broken U(1) symmetry. In the long-range limit of twocomponent Bose-Einstein condensates, the vortices from different condensates experience mutual dissipative dynamics unless their cores overlap precisely. For comparison, we also consider a close Hermitian analog of the system and demonstrate that the non-Hermitian two-component model possesses much richer dynamics than its Hermitian counterpart.

The Journal of Physical Chemistry B

EPJ Web of Conferences, 2018

We simulate lattice QCD with two flavors of Wilson fermions at imaginary baryon chemical potentia... more We simulate lattice QCD with two flavors of Wilson fermions at imaginary baryon chemical potential. Results for the baryon number density computed in the confining and deconfining phases at imaginary baryon chemical potential are used to determine the baryon number density and higher cumulants at the real chemical potential via analytical continuation.

Physical Review Letters, 2018

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principl... more We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principle numerical simulations. Working in two spatial dimensions at zero temperature we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.

Physical Review Letters, 2018

We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principl... more We study, for the first time, the Casimir effect in non-Abelian gauge theory using first-principle numerical simulations. Working in two spatial dimensions at zero temperature we find that closely spaced perfect chromoelectric conductors attract each other with a small anomalous scaling dimension. At large separation between the conductors, the attraction is exponentially suppressed by a new massive quantity, the Casimir mass, which is surprisingly different from the lowest glueball mass. The apparent emergence of the new massive scale may be a result of the backreaction of the vacuum to the presence of the plates as sufficiently close chromoelectric conductors induce, in a space between them, a smooth crossover transition to a color deconfinement phase.