Dimensional compactification and two‐particle binding

Delfino, A.; Timóteo, V. S.; Frederico, T.; Tomio, Lauro; Cordeiro, Claudette

doi:10.1002/qua.22625

Cited by 3 publications

(2 citation statements)

References 74 publications

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“…The x-direction, which points out of the page, is always taken to be infinite. 5 An alternative means of moving continuously among various dimensions is to constrain two-particle scattering to a cylinder of radius R and to consider the limit of a plane (  ¥ R ) and of a wire (  R 0) as is relevant in the case of a carbon nanotube [15]. order of consideration.…”

Section: Compactificationmentioning

confidence: 99%

Dimensional crossover in non-relativistic effective field theory

Beane

Jafry

2019

J. Phys. B: At. Mol. Opt. Phys.

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Isotropic scattering in various spatial dimensions is considered for arbitrary finiterange potentials using non-relativistic effective field theory. With periodic boundary conditions, compactifications from a box to a plane and to a wire, and from a plane to a wire, are considered by matching S-matrix elements. The problem is greatly simplified by regulating the ultraviolet divergences using dimensional regularization with minimal subtraction. General relations among (all) effective-range parameters in the various dimensions are derived, and the dependence of bound states on changing dimensionality are considered. Generally, it is found that compactification binds the two-body system, even if the uncompactified system is unbound. For instance, compactification from a box to a plane gives rise to a bound state with binding momentum given by ln 1 2 3 + √ 5 in units of the inverse compactification length. This binding momentum is universal in the sense that it does not depend on the two-body interaction in the box. When the two-body system in the box is at unitarity, the Smatrices of the compactified two-body system on the plane and on the wire are given exactly as universal functions of the compactification length.

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Section: Compactificationmentioning

confidence: 99%

Dimensional crossover in non-relativistic effective field theory

Beane

Jafry

2019

J. Phys. B: At. Mol. Opt. Phys.

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“…Due to the absence of an analytical solution for the Coulomb problem on a cylinder, it was previously studied with the use of various approximation methods such as the variational approach [19][20][21] or scattering formalism [22]. There are two distinctive regimes between 2D and 1D limits which are characterized by large and small radius values, respectively.…”

Section: Introductionmentioning

confidence: 99%

Coulomb problem on single- and double-wall cylinders

Deinega¹,

Voronova²,

Lozovik³

2012

J. Phys.: Condens. Matter

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In this paper we calculate the energies of ground and excited states of two opposite charge carriers confined on a single- or double-wall cylindrical surface. A nontrivial dependence of excited state energies on cylinder radius value (for the case of a single-wall cylinder) is found, and the explanation of this behavior is based on symmetry properties of the corresponding wavefunctions. The crossover from a one-dimensional problem to a two-dimensional one with increase of the radius value is discussed in detail. For the double-wall cylinder, we obtain and analyze the dependence of ground state energy on interwall distance and ratio between particle masses.

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