arXiv subjects

Eugene B. Kolomeisky

Publications and source records attributed to Eugene B. Kolomeisky.

At least 55 records · Page 3Linked to original sources

arXiv2008

Geometrical interpretation of the Casimir effect

Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be efficiently computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of the Dirichlet geometries. For the planar case a finite universal force is automatically found. Consistent with other calculations of the effect, for curved geometries divergent (non-universal) expressions are encountered. They are interpreted geometrically following Candelas and Deutsch (1979) as largely due to the divergent self-energy of the boundary contributing to the force. This viewpoint is supported by explicit calculations for a wedge-circular arc geometry in two dimensions where non-universal and universal contributions into the effect can be unambiguously separated. We also give a heuristic derivation of the purely geometrical expression (Sen, 1981) for the non-universal piece of the Casimir energy due to an arbitrary smooth two-dimensional Dirichlet boundary of a compact region.

cond-mat.stat-mech↗

arXiv2008

Casimir effect in a one-dimensional gas of free fermions

We compute an analog Casimir effect in a one-dimensional spinless Luttinger liquid confined to a segment in the presence of a nearly-impenetrable partition dividing the segment into two compartments. The Casimir interaction is found to be a bounded piecewise-continuous oscillatory function whose maxima are points of force discontinuity and correspond to resonant tunneling across the partition. The well-known regularization-based results are reproduced by the lower envelope of this function, which corresponds to an approximation that ignores the rather large oscillations due to particle discreteness. These macroscopic conclusions are tested and confirmed via a rigorous analysis of the Casimir effect in an exactly-solvable model of a one-dimensional non-relativistic spinless gas of free fermions, thus resolving an objection that has been raised by Volovik (2003). Additionally we confirm the result of a recent calculation which employed an effective low-energy theory with a cutoff to find the Casimir interaction between two strong well-separated impurities placed in a Luttinger liquid.

cond-mat.mes-hall↗

arXiv2007

On the calculation of the Casimir forces

Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of geometries. For the planar case a finite universal force is automatically found. For curved geometries formally divergent expressions are encountered which we argue are largely due to the divergent self-energy of the boundary contributing to the force. This idea is supported by computing the effect for a fixed perimeter wedge-arc geometry in two dimensions.

cond-mat.stat-mech↗

arXiv2007

Interacting bosons in a nearly-resonant potential well

We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for repulsive particles and a super-threshold trapping potential the equilibrium number of bound bosons and the size of the ground state diverge upon approaching the single-particle threshold from above. For attractive interactions and a sub-threshold trap a collective bound state always forms for a sufficiently large number of bosons despite the inability of interparticle attraction alone to form a two-body bound state.

cond-mat.other↗

arXiv2006

Ground-state properties of a large Coulomb-blockaded quantum dot

Using renormalization-group techniques we analyze equilibrium properties of a large gated quantum dot coupled via a long and narrow channel to a reservoir of electrons. Treating the electrons in the channel as one-dimensional and interacting, we demonstrate that for nearly-open dot and not very strong spin fluctuations the ground-state properties as a function of the gate voltage are non-analytic at the points of half-integer average dot population. Specifically, the exact result of K. A. Matveev, Phys. Rev. B 51, 1743 (1995), that the dot capacitance shows periodic logarithmic singularities is rederived as a special case corresponding to non-interacting electrons. We demonstrate that this conclusion also holds in the presence of SU(2) spin symmetry, and argue that logarithmic singularities persist as long as the Coulomb blockade is destroyed which will be the case for sufficiently large tunneling and not very strong interparticle repulsions. We show that interparticle repulsions aid the Coulomb blockade to survive disordering effect of zero-point motion provided the tunneling is sufficiently weak. Upon increase of tunneling, the Coulomb blockade disappears through a Kosterlitz-Thouless phase transition characterized by a dot population jump whose magnitude is only determined by interparticle repulsions in the channel. Similar conclusions are applicable to systems without SU(2) spin symmetry except that the logarithmic singularity of the capacitance is replaced by a power-law non-analyticity whose exponent characterizes the degree of spin fluctuations.

cond-mat.mes-hall↗

arXiv2005

Quantum dissociation of an edge of a Luttinger liquid

In a Luttinger liquid phase of one-dimensional molecular matter the strength of zero-point motion can be characterized by dimensionless De Boer's number quantifying the interplay of quantum fluctuations and two-body interactions. Selecting the latter in the Morse form we show that dissociation of the Luttinger liquid is a process initiated at the system edge. The latter becomes unstable against quantum fluctuations at a value of De Boer's number which is smaller than that of the bulk instability which parallels the classical phenomenon of surface melting.

cond-mat.mtrl-sci↗

arXiv2005

The Zel'dovich effect and evolution of atomic Rydberg spectra along the Periodic Table

In 1959 Ya. B. Zel'dovich predicted that the bound-state spectrum of the non-relativistic Coulomb problem distorted at small distances by a short-range potential undergoes a peculiar reconstruction whenever this potential alone supports a low-energy scattering resonance. However documented experimental evidence of this effect has been lacking. Previous theoretical studies of this phenomenon were confined to the regime where the range of the short-ranged potential is much smaller than Bohr's radius of the Coulomb field. We go beyond this limitation by restricting ourselves to highly-excited s states. This allows us to demonstrate that along the Periodic Table of elements the Zel'dovich effect manifests itself as systematic periodic variation of the Rydberg spectra with a period proportional to the cubic root of the atomic number. This dependence, which is supported by analysis of experimental and numerical data, has its origin in the binding properties of the ionic core of the atom.

physics.atom-ph↗

arXiv2003

Ground-state properties of artificial bosonic atoms, Bose interaction blockade and the single-atom pipette

We analyze the ground-state properties of an artificial atom made out of repulsive bosons attracted to a center for the case that all the interactions are short-ranged. Such bosonic atoms could be created by optically trapping ultracold particles of alkali vapors; we present the theory describing how their properties depend on experimentally adjustable strength of ``nuclear'' attraction and interparticle repulsion. The binding ability of the short-range potential increases with space dimensionality - only a limited number of particles can be bound in one dimension, while in two and three dimensions the number of bound bosons can be chosen at will. Particularly in three dimensions we find an unusual effect of enhanced resonant binding: for not very strong interparticle repulsion the equilibrium number of bosons bound to a nuclear potential having a sufficiently shallow single-particle state increases without bound as the nuclear potential becomes less attractive. As a consequence of the competing nuclear attraction enhanced by the Bose statistics and interparticle repulsions, the dependence of the ground-state energy of the atom on the number of particles has a minimum whose position is experimentally tunable. This implies a staircase dependence of the equilibrium number of bound bosons on external parameters which may be used to create a single-atom pipette - an arrangement which allows the transport of atoms into and out of a reservoir, one at a time.

cond-mat↗

arXiv2002

Ground-state properties of one-dimensional matter and quantum dissociation of a Luttinger liquid

We analyze ground-state properties of strictly one-dimensional molecular matter comprised of identical particles of mass m. Such a class of systems can be described by an additive two-body potential whose functional form is common to all substances which only differ in the energy εand range l scales of the potential. With this choice De Boer's quantum theorem of corresponding states holds thus implying that ground-state properties expressed in appropriate reduced form are only determined by the dimensionless parameter λ_{0}^{2} \sim \hbar^{2}/ml^{2}εmeasuring the strength of zero-point motion in the system. The presence of a minimum in the two-body interaction potential leads to a many-body bound state which is a Luttinger liquid. As λ_{0} increases, the asymmetry of the two-body potential causes quantum expansion, softening, and eventual evaporation of the Luttinger liquid into a gas phase. Selecting the pair interaction potential in the Morse form we analytically compute the properties of the Luttinger liquid and its range of existence. As lambda_{0} increases, the system first undergoes a discontinuous evaporation transition into a diatomic gas followed by a continuous dissociation transition into a monoatomic gas. In particular we find that spin-polarized isotopes of hydrogen and He-3 are monoatomic gases, He-4 is a diatomic gas, while molecular hydrogen and heavier substances are Luttinger liquids. We also investigate the effect of finite pressure on the properties of the liquid and monoatomic gas phases. In particular we estimate a pressure at which molecular hydrogen undergoes an inverse Peierls transition into a metallic state which is a one-dimensional analog of the transition predicted by Wigner and Huntington in 1935.

cond-mat↗

arXiv2002

Quantum fluctuations of charge and phase transitions of a large Coulomb-blockaded quantum dot

We analyze ground-state properties of a large gated quantum dot coupled via a quantum point contact to a reservoir of one-dimensional interacting spinless electrons. We find that the classical step-like dependence of the dot population on the gate voltage is preserved under certain conditions. We point out that the problem is related to the classical one-dimensional Ising model with inverse-square interactions. This Ising universality class further subdivides into (i) the Kondo/Ising class and (ii) the tricritical class. For systems of the Kondo/Ising class, and repulsive electrons, the gate voltage dependence of the dot population is continuous for sufficiently open dots, while taking the form of a modified staircase for dots sufficiently isolated from the reservoir. At the phase transition between the two regimes the magnitude of the dot population jump is universal. For systems in the tricritical class we find in addition an intermediate regime where the dot population jumps from near integer value to a region of stable population centered about a half-integer value. In particular, this tricritical behaviour (together with the two dependencies already seen in the Kondo/Ising class) is realized for non-interacting electrons.

cond-mat↗

arXiv2001

Reply to `Comment on "Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation"'

This is a published reply to the comment of Bhaduri and Sen, Physical Review Letters 86, 4708 (2001), cond-mat/0105385, on our original work, Physical Review Letters 85, 1146 (2000), cond-mat/0002282 . In this reply we point out that our continuum theory captures the correct physics of non-interacting fermions in one dimension. In contrast, the two proposed alternative theories of Bhaduri and Sen produce physically incorrect results. We take this opportunity to point out that the abstract of cond-mat/0105385 obscures the contents of the comment and reply. The soliton solutions found in our theory are the continuum analogs of solitonic states which are known from exact studies of non-interacting fermions.

cond-mat.stat-mech↗

arXiv2001

How to split the electron in one dimension

Using the example of the Davydov soliton - a large acoustic polaron in one dimension - we demonstrate that the electron wave function can be fissioned in two or more long-lived, well-localized and spatially arbitrarily far separated fragments. The phenomenon of wave function splitting is a result of the electron-medium interaction, and takes place under a variety of conditions provided the initial wave function of the electron is localized and has at least one node.

cond-mat↗

arXiv2000

The Bose molecule in one dimension

We give the Green function, momentum distribution, two-particle correlation function, and structure factor for the bound state of N indistinguishable bosons with an attractive delta-function interaction in one dimension, and an argument showing that this boson "molecule" has no excited states other than dissociation into separated pieces.

cond-mat.stat-mech↗

arXiv2000

Superfluid Hydrodynamics of an Electron Gas in a Superstrong Magnetic Field

We derive the equations of hydrodynamics of a fully polarized electron gas placed in a strong magnetic field. These equations reveal the existence of solitons - immobile or propagating domain wall-like defects whose plane is perpendicular to the field direction. The solitons are used to construct weakly excited states, and novel nonuniform persistent current states of the system.

cond-mat↗

arXiv2000

Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d less than or equal to 2, and we propose the appropriate low-dimensional modifications. For d=1 we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.

cond-mat.stat-mech↗

arXiv2000

Breaking a one-dimensional chain: fracture in 1 + 1 dimensions

The breaking rate of an atomic chain stretched at zero temperature by a constant force can be calculated in a quasiclassical approximation by finding the localized solutions ("bounces") of the equations of classical dynamics in imaginary time. We show that this theory is related to the critical cracks of stressed solids, because the world lines of the atoms in the chain form a two-dimensional crystal, and the bounce is a crack configuration in (unstable) mechanical equilibrium. Thus the tunneling time, Action, and breaking rate in the limit of small forces are determined by the classical results of Griffith. For the limit of large forces we give an exact bounce solution that describes the quantum fracture and classical crack close to the limit of mechanical stability. This limit can be viewed as a critical phenomenon for which we establish a Levanyuk-Ginzburg criterion of weakness of fluctuations, and propose a scaling argument for the critical regime. The post-tunneling dynamics is understood by the analytic continuation of the bounce solutions to real time.

cond-mat.stat-mech↗

arXiv1999

Self-localization of directed polymers and oppressive population control

We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We also map this system to a model of population dynamics with fixed total population. Our previous results translate to static and expanding population clusters, depending on the birth and death rates. A novel ``pseudo-travelling wave'' is observed in some sectors of parameter space.

cond-mat.stat-mech↗

arXiv1999

Manifold self-localization in a deformable medium

Directed manifolds (domain walls, interfaces, vortex lines) in a deformable medium can exist in a correlated state in which the manifold is self-localized by its own strain field. Depending on the temperature, manifold/medium dimensionalities, and the strength of the coupling with the medium, the degree of localization of the ground state can vary both continuously and discontinuously; there can be phase transitions from self- localized to the free-manifold state.

cond-mat.stat-mech↗