Efimov physics from a renormalization group perspective

Hammer, H.-W.; Platter, Lucas

doi:10.1098/rsta.2011.0001

Cited by 28 publications

(27 citation statements)

References 100 publications

(201 reference statements)

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“…• using the running of ground-state energies of nuclei with resolution scales to estimate errors, identify correlations and diagnosing missing many-body forces (e.g., Tjon lines) [128,129,32,70,64];…”

Section: Discussionmentioning

confidence: 99%

New applications of renormalization group methods in nuclear physics

2013

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Abstract. We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

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Section: Discussionmentioning

confidence: 99%

New applications of renormalization group methods in nuclear physics

2013

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“…8 As many have observed [28][29][30][31][32][33][34][35][36][37][38][39][40] because of this the Schrödinger Hamiltonian can fail to be self-adjoint, depending the boundary conditions that hold at r = . Selecting a choice of boundary condition to secure its self-adjointness -not a unique construction -is known as constructing its self-adjoint extension [41][42][43][44][45][46][47][48].…”

Section: Jhep07(2017)072mentioning

confidence: 99%

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Burgess

Hayman

Rummel

et al. 2017

J. High Energ. Phys.

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We apply point-particle effective field theory (PPEFT) to compute the leading shifts due to finite-sized source effects in the Coulomb bound energy levels of a relativistic spinless charged particle. This is the analogue for spinless electrons of calculating the contribution of the charge-radius of the source to these levels, and our calculation disagrees with standard calculations in several ways. Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size, one of which captures the standard charge-radius contribution. The other effective operator is a contact interaction whose leading contribution to δE arises linearly (rather than quadratically) in the small length scale, , characterizing the finite-size effects, and is suppressed by (Zα) 5 . We argue that standard calculations miss the contributions of this second operator because they err in their choice of boundary conditions at the source for the wave-function of the orbiting particle. PPEFT predicts how this boundary condition depends on the source's charge radius, as well as on the orbiting particle's mass. Its contribution turns out to be crucial if the charge radius satisfies (Zα) 2 a B , where a B is the Bohr radius, because then relativistic effects become important for the boundary condition. We show how the problem is equivalent to solving the Schrödinger equation with competing Coulomb, inverse-square and delta-function potentials, which we solve explicitly. A similar enhancement is not predicted for the hyperfine structure, due to its spin-dependence. We show how the charge-radius effectively runs due to classical renormalization effects, and why the resulting RG flow is central to predicting the size of the energy shifts (and is responsible for its being linear in the source size). We discuss how this flow is relevant to systems having much larger-than-geometric cross sections, such as those with large scattering lengths and perhaps also catalysis of reactions through scattering with monopoles. Experimental observation of these effects would require more precise measurement of energy levels for mesonic atoms than are now possible.

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“…This trigged the fruitful field of Efimov physics in three dimensions. [7][8][9][10] In two dimensions, the counterpart is studied for the case of three interacting bosons [11][12][13][14][15] and charged particles.…”

Section: Introductionmentioning

confidence: 99%

Three-boson bound states in two dimensions

Ren

Aleǐner

2017

Phys. Rev. B

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We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in heterostructures or dihalogenated materials). The bosons are classified in two species (a,b) such that a-a and b-b pairs repel each other and a-b attract each other, forming the two-particle bound state with binding energy (such as bi-exciton). We developed an efficient routine based on the proper choice of basis for analytic and numerical calculations. For zero-angular momentum we found the energies of the three-particle bound statesfor wide ranges of the scattering lengths, and found a universal curve ofwhich depends only on the scattering lengths but not the microscopic details of the interactions.

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Efimov physics from a renormalization group perspective

Abstract: We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.

Cited by 28 publications

References 100 publications

New applications of renormalization group methods in nuclear physics

New applications of renormalization group methods in nuclear physics

Point-particle effective field theory II: relativistic effects and Coulomb/inverse-square competition

Three-boson bound states in two dimensions

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