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Dmitry K. Gridnev

Publications and source records attributed to Dmitry K. Gridnev.

15 recordsLinked to original sources
arXiv2016

Manifestation of Universality in the Asymmetric Helium Trimer and in the Halo Nucleus $^{22}$C

We prove that the corner angle distributions in the bound three-body system AAB, which consists of two particles of type A and one particle of type B, approach universal form if the pair AA has a virtual state at zero energy and the binding energy of AAB goes to zero. We derive explicit expressions for the universal corner angle distributions in terms of elementary functions, which depend solely on the mass ratio m(A)/m(B) and do not depend on pair interactions. On the basis of experimental data and calculations we demonstrate that such systems as the asymmetric Helium trimer $^3$He$^4$He$_2$ and the halo nucleus $^{22}$C exhibit universal features. Thus our result establishes an interesting link between atomic and nuclear physics through the few-body universality.

nucl-th↗
arXiv2015

Universal low-energy behavior in three-body systems

We consider a pairwise interacting quantum 3-body system in 3-dimensional space with finite masses and the interaction term $V_{12} + λ(V_{13} + V_{23})$, where all pair potentials are assumed to be nonpositive. The pair interaction of the particles $\{1,2\}$ is tuned to make them have a zero energy resonance and no negative energy bound states. The coupling constant $λ>0$ is allowed to take the values for which the particle pairs $\{1,3\}$ and $\{2,3\}$ have no bound states with negative energy. Let $λ_{cr}$ denote the critical value of the coupling constant such that $E(λ) \to -0$ for $λ\to λ_{cr}$, where $E(λ)$ is the ground state energy of the 3-body system. We prove the theorem, which states that near $λ_{cr}$ one has $E(λ) = C (λ-λ_{cr})[\ln (λ-λ_{cr})]^{-1}+$h.t., where $C$ is a constant and h.t. stands for "higher terms". This behavior of the ground state energy is universal (up to the value of the constant $C$), meaning that it is independent of the form of pair interactions.

math-ph↗
arXiv2014

Proof of the Super Efimov Effect

We consider the system of 3 nonrelativistic spinless fermions in two dimensions, which interact through spherically-symmetric pair interactions. Recently a claim has been made for the existence of the so-called super Efimov effect [Y. Nishida et al., Phys. Rev. Lett. 110, 235301 (2013)]. Namely, if the interactions in the system are fine-tuned to a p-wave resonance, an infinite number of bound states appears, whose negative energies are scaled according to the double exponential law. We present the mathematical proof that such system indeed has an infinite number of bound levels. We also prove that $\lim_{E \to 0} |\ln|\ln E||^{-1} N(E) = 8/(3π) $, where $N(E)$ is the number of bound states with the energy less than $-E <0$. The value of this limit is equal exactly to the value derived in [Y. Nishida et al.] using renormalization group approach. Our proof resolves a recent controversy about the validity of results in [Y. Nishida et al.].

math-ph↗
arXiv2014

Nuclear interactions with modern three-body forces lead to the instability of neutron matter and neutron stars

It is shown that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of $N$ neutrons $E(N)$, which interact through these forces, we prove mathematically that $E(N) = -cN^3 + \mathcal{O}(N^{8/3})$, where $c>0$ is a constant. This means that: (i) the energy per particle and neutron density diverge rapidly for large neutron numbers; (ii) bound states of $N$ neutrons exist for $N$ large enough. The neutron matter collapse is possible due to the form of the repulsive core in three-body forces, which vanishes when three nucleons occupy the same site in space. The old variant of the forces Urbana VI, where the phenomenological repulsive core does not vanish at the origin, resolves this problem. We prove that to prevent the collapse one should add a repulsive term to the Urbana IX potential, which should be larger than 50 MeV when 3 nucleons occupy the same spatial position.

nucl-th↗
arXiv2013

Universal Angular Probability Distribution of Three Particles near Zero Energy Threshold

We study bound states of a 3--particle system in $\mathbb{R}^3$ described by the Hamiltonian $H(λ_n) = H_0 + v_{12} + λ_n (v_{13} + v_{23})$, where the particle pair $\{1,2\}$ has a zero energy resonance and no bound states, while other particle pairs have neither bound states nor zero energy resonances. It is assumed that for a converging sequence of coupling constants $λ_n \to λ_{cr}$ the Hamiltonian $H(λ_n)$ has a sequence of levels with negative energies $E_n$ and wave functions $ψ_n$, where the sequence $ψ_n$ totally spreads in the sense that $\lim_{n \to \infty}\int_{|ζ| \leq R} |ψ_n (ζ)|^2 dζ= 0$ for all $R>0$. We prove that for large $n$ the angular probability distribution of three particles determined by $ψ_n$ approaches the universal analytical expression, which does not depend on pair--interactions. The result has applications in Efimov physics and in the physics of halo nuclei.

math-ph↗
arXiv2013

Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum

We consider a system of $N$ pairwise interacting particles described by the Hamiltonian $H$, where $σ_{ess} (H) = [0,\infty)$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs and obey certain restrictions regarding the fall off. It is proved that if $N \geq 4$ and none of the Hamiltonians corresponding to the subsystems containing $N-2$ or less particles has an eigenvalue equal to zero then $H$ has a finite number of negative energy bound states. This result provides a positive proof to a long--standing conjecture of Amado and Greenwood stating that four bosons with an empty negative continuous spectrum have at most a finite number of negative energy bound states. Additionally, we give a short proof to the theorem of Vugal'ter and Zhislin on the finiteness of the discrete spectrum and pose a conjecture regarding the existence of the "true" four--body Efimov effect.

math-ph↗
arXiv2013

Selecting fast folding proteins by their rate of convergence

We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using only the very initial parts of the dynamical trajectories. It does not require any preliminary knowledge of the native state and can be applied to different kinds of models, including atomistic descriptions. We tested the method within both the lattice and off-lattice model frameworks and obtained several so far unknown good folders. The unbiased algorithm also allows to determine the optimal folding temperature and takes at least 3--4 orders of magnitude less time steps than those needed to compute folding times.

physics.bio-ph↗
arXiv2012

The few-body universality is not exact for more than three particles

In the literature it is conjectured that the ground state energies of three and four bosons are universally related for all pair-interactions given that two bosons have a zero energy resonance and no negative energy bound states. Here it is proved analytically that such relation cannot be exact.

math-ph↗
arXiv2012

Bound States at Threshold resulting from Coulomb Repulsion

The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction on the particle statistics is imposed. It is proved that if the lowest dissociation threshold corresponds to the decay into two likewise non-zero charged clusters then the bound state, which approaches the threshold, does not spread and eventually becomes the bound state at threshold. The obtained results have applications in atomic and nuclear physics. In particular, we prove that atomic ion with atomic critical charge $Z_{cr}$ and $N_e$ electrons has a bound state at threshold given that $Z_{cr} \in (N_e -2, N_e -1)$, whereby the electrons are treated as fermions and the mass of the nucleus is finite.

math-ph↗
arXiv2012

Essential spectrum of a limit of self--adjoint operators

For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.

math-ph↗
arXiv2012

Zero Energy Bound States and Resonances in Three--Particle Systems

We consider a three-particle system in $\mathbb{R}^3$ with non-positive pair-potentials and non-negative essential spectrum. Under certain restrictions on potentials it is proved that the eigenvalues are absorbed at zero energy threshold given that there is no negative energy bound states and zero energy resonances in particle pairs. It is shown that the condition on the absence of zero energy resonances in particle pairs is essential. Namely, we prove that if at least one pair of particles has a zero energy resonance then a square integrable zero energy ground state of three particles does not exist. It is also proved that one can tune the coupling constants of pair potentials so that for any given $R, ε>0$: (a) the bottom of the essential spectrum is at zero; (b) there is a negative energy ground state $ψ(ξ)$ such that $\int |ψ(ξ)|^2 d^6 ξ= 1$ and $\int_{|ξ| \leq R} |ψ(ξ)|^2 d^6 ξ< ε$.

math-ph↗
arXiv2011

Zero Energy Bound States in Many--Particle Systems

It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs.

math-ph↗
arXiv2010

Zero Energy Bound States in Three--Particle Systems

Under certain restrictions on pair--potentials it is proved that the eigenvalues in the three--particle system are absorbed at zero energy threshold if there is no negative energy bound states and zero energy resonances in particle pairs.

math-ph↗
arXiv2010

Zero Energy Ground State in the Three-Body System

We consider a 3--body system in $\mathbb{R}^3$ with non--positive potentials and non--negative essential spectrum. Under certain requirements on the fall off of pair potentials it is proved that if at least one pair of particles has a zero energy resonance then a square integrable zero energy ground state of three particles does not exist. This complements the analysis in \cite{1}, where it was demonstrated that square integrable zero energy ground states are possible given that in all two--body subsystems there is no negative energy bound states and no zero energy resonances. As a corollary it is proved that one can tune the coupling constants of pair potentials so that for any given $R, ε>0$: (a) the bottom of the essential spectrum is at zero; (b) there is a negative energy ground state $ψ(ξ)$, where $\int |ψ(ξ)|^2 = 1$; (c) $\int_{|ξ| \leq R} |ψ(ξ)|^2 < ε$.

math-ph↗