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Publications (10 of 21) Show all publications
Lundholm, D. & Seiringer, R. (2018). Fermionic behavior of ideal anyons. Letters in Mathematical Physics, 108(11), 2523-2541
Open this publication in new window or tab >>Fermionic behavior of ideal anyons
2018 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 108, no 11, p. 2523-2541Article in journal (Refereed) Published
Abstract [en]

We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter alpha. The lower bounds extend to Lieb-Thirring inequalities for all anyons except bosons.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Intermediate quantum statistics, Magnetic interaction, Ideal anyon gas, Lieb-Thirring inequality
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-237086 (URN)10.1007/s11005-018-1091-y (DOI)000446491500008 ()2-s2.0-85046717412 (Scopus ID)
Funder
Swedish Research Council, 2013-4734EU, Horizon 2020, 694227
Note

QC 20181022

Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2018-10-24Bibliographically approved
Correggi, M., Lundholm, D. & Rougerie, N. (2018). Local density approximation for almost-bosonic anyons. Contemporary Mathematics, 717, 77-92
Open this publication in new window or tab >>Local density approximation for almost-bosonic anyons
2018 (English)In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 717, p. 77-92Article in journal (Refereed) Published
Abstract [en]

We discuss the average-field approximation for a trapped gas of non-interacting anyons in the quasi-bosonic regime. In the homogeneous case, i.e., for a confinement to a bounded region, we prove that the energy in the regime of large statistics parameter, i.e., for “less-bosonic” anyons, is independent of boundary conditions and of the shape of the domain. When a non-trivial trapping potential is present, we derive a local density approximation in terms of a Thomas-Fermi-like model. The results presented here mainly summarize [Anal. PDE 10 (2017), 1169-1200] with additional remarks and strengthening of some statements.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-246517 (URN)10.1090/conm/717/14442 (DOI)000465195200006 ()2-s2.0-85059770658 (Scopus ID)
Note

QC 20190321

Available from: 2019-03-21 Created: 2019-03-21 Last updated: 2019-10-18Bibliographically approved
Lundholm, D. & Rougerie, N. (2016). Emergence of Fractional Statistics for Tracer Particles in a Laughlin Liquid [Letter to the editor]. Physical Review Letters, 116(17), Article ID 170401.
Open this publication in new window or tab >>Emergence of Fractional Statistics for Tracer Particles in a Laughlin Liquid
2016 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 116, no 17, article id 170401Article in journal, Letter (Refereed) Published
Abstract [en]

We consider a thought experiment where two distinct species of 2D particles in a perpendicular magnetic field interact via repulsive potentials. If the magnetic field and the interactions are strong enough, one type of particles forms a Laughlin state and the other type couples to Laughlin quasiholes. We show that, in this situation, the motion of the second type of particles is described by an effective Hamiltonian, corresponding to the magnetic gauge picture for noninteracting anyons. The argument is in accord with, but distinct from, the Berry phase calculation of Arovas, Schrieffer, and Wilczek. It suggests possibilities to observe the influence of effective anyon statistics in fractional quantum Hall systems.

Place, publisher, year, edition, pages
American Physical Society, 2016
Keywords
anyons, fractional statistics, fractional quantum Hall effect, Laughlin quasiparticles, emergent statistics, magnetic interaction
National Category
Condensed Matter Physics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:kth:diva-186069 (URN)10.1103/PhysRevLett.116.170401 (DOI)000374964400001 ()2-s2.0-84964768878 (Scopus ID)
Projects
VR 2013-4734: Spectral theory of quantum systems with exotic symmetries
Funder
Swedish Research Council, 2013-4734
Note

QC 20160503

Available from: 2016-04-29 Created: 2016-04-29 Last updated: 2017-11-30Bibliographically approved
Lundholm, D., Nam, P. T. & Portmann, F. (2016). Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems. Archive for Rational Mechanics and Analysis, 219(3), 1343-1382
Open this publication in new window or tab >>Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems
2016 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 219, no 3, p. 1343-1382Article in journal (Refereed) Published
Abstract [en]

We prove analogues of the Lieb-Thirring and Hardy-Lieb-Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
Lieb-Thirring inequality, many-body quantum mechanics, uncertainty principle, exclusion principle, interpolation inequality, fractional Laplacian
National Category
Mathematical Analysis
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-176067 (URN)10.1007/s00205-015-0923-5 (DOI)000368535400010 ()2-s2.0-84954367932 (Scopus ID)
Projects
VR 2013-4734: Spectral theory of quantum systems with exotic symmetries
Funder
Swedish Research Council, 67801Knut and Alice Wallenberg Foundation, KAW 2010.0063EU, European Research Council, 321029Swedish Research Council, 2013-4734
Note

QC 20160220

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approved
Lundholm, D. (2015). Geometric extensions of many-particle Hardy inequalities. Journal of Physics A: Mathematical and Theoretical, 48(17), Article ID 175203.
Open this publication in new window or tab >>Geometric extensions of many-particle Hardy inequalities
2015 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 17, article id 175203Article in journal (Refereed) Published
Abstract [en]

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of R^n. This includes geometric extensions of the standard Hardy inequalities to involve volumes of simplices spanned by a subset of points. Clifford/multilinear algebra is employed to simplify geometric computations. These results and the techniques involved are relevant for classes of exactly solvable quantum systems such as the Calogero-Sutherland models and their higher-dimensional generalizations, as well as for membrane matrix models, and models of more complicated particle interactions of geometric character.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2015
Keywords
uncertainty principle, many-body interactions, Hardy inequality, Calogero-Sutherland models, Clifford algebra
National Category
Mathematical Analysis
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-163789 (URN)10.1088/1751-8113/48/17/175203 (DOI)000352358100005 ()2-s2.0-84928895604 (Scopus ID)
Note

QC 20150518

Available from: 2015-04-12 Created: 2015-04-12 Last updated: 2017-12-04Bibliographically approved
Lundholm, D., Portmann, F. & Solovej, J. P. (2015). Lieb-Thirring Bounds for Interacting Bose Gases. Communications in Mathematical Physics, 335(2), 1019-1056
Open this publication in new window or tab >>Lieb-Thirring Bounds for Interacting Bose Gases
2015 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 335, no 2, p. 1019-1056Article in journal (Refereed) Published
Abstract [en]

We study interacting Bose gases and prove lower bounds for the kinetic plus interaction energy of a many-body wave function in terms of its particle density. These general estimates are then applied to various types of interactions, including hard sphere (in 3D) and hard disk (in 2D) as well as a general class of homogeneous potentials.

Keywords
Interacting Bose gas, quantum many-body problem, energy inequalities, Lieb-Thirring inequalities, local exclusion principle, local uncertainty principle, hard-sphere interaction, hard-disk interaction, homogeneous potentials, scattering length
National Category
Mathematical Analysis Condensed Matter Physics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-145067 (URN)10.1007/s00220-014-2278-4 (DOI)000350367700015 ()2-s2.0-84925493862 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation, KAW 2010.0063Swedish Research Council, 2013-4734 2012-3864EU, European Research Council, 321029
Note

QC 20150408. Updated from manuscript to article in journal.

Available from: 2014-05-07 Created: 2014-05-07 Last updated: 2017-12-05Bibliographically approved
Lundholm, D. & Rougerie, N. (2015). The Average Field Approximation for Almost Bosonic Extended Anyons. Journal of statistical physics, 161, 1236-1267
Open this publication in new window or tab >>The Average Field Approximation for Almost Bosonic Extended Anyons
2015 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, p. 1236-1267Article in journal (Refereed) Published
Abstract [en]

Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter α is proportional to N−1 when N→∞. This means that the statistics is seen as a “perturbation from the bosonic end”. We model this situation in the magnetic gauge picture by bosons interacting through long-range magnetic potentials. We assume that these effective statistical gauge potentials are generated by magnetic charges carried by each particle, smeared over discs of radius R (extended anyons). Our method allows to take R→0 not too fast at the same time as N→∞. In this limit we rigorously justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2015
Keywords
Anyons, Fractional statistics, Magnetic interaction, Mean-field theory, Quantum de Finetti theorem
National Category
Mathematical Analysis Condensed Matter Physics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-176070 (URN)10.1007/s10955-015-1382-y (DOI)000365187700009 ()2-s2.0-84947027030 (Scopus ID)
Projects
VR 2013-4734:Spectral theory of quantum systems with exotic symmetries
Funder
Swedish Research Council, 67801, 2013-4734Knut and Alice Wallenberg Foundation, KAW 2010.0063
Note

QC 20151218

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approved
Lundholm, D. & Solovej, J. P. (2014). Local Exclusion and Lieb-€“Thirring Inequalities for Intermediate and Fractional Statistics. Annales de l'Institute Henri Poincare. Physique theorique, 15(6), 1061-1107
Open this publication in new window or tab >>Local Exclusion and Lieb-€“Thirring Inequalities for Intermediate and Fractional Statistics
2014 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 15, no 6, p. 1061-1107Article in journal (Refereed) Published
Abstract [en]

In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb–Thirring inequality for anyons in two dimensions, and derive new Lieb–Thirring inequalities for intermediate statistics in one dimension with implications for models of Lieb–Liniger and Calogero–Sutherland type. These inequalities follow from a local form of the exclusion principle valid for such generalized exchange statistics.

Place, publisher, year, edition, pages
Birkhauser Verlag, 2014
National Category
Mathematical Analysis Condensed Matter Physics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-179451 (URN)10.1007/s00023-013-0273-5 (DOI)000335979500002 ()2-s2.0-84901228703 (Scopus ID)
Note

QC 20160119

Available from: 2015-12-16 Created: 2015-12-16 Last updated: 2017-12-01Bibliographically approved
Lundholm, D. & Solovej, J. P. (2013). Hardy and Lieb-Thirring Inequalities for Anyons. Communications in Mathematical Physics, 322(3), 883-908
Open this publication in new window or tab >>Hardy and Lieb-Thirring Inequalities for Anyons
2013 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 322, no 3, p. 883-908Article in journal (Refereed) Published
Abstract [en]

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter α∈[0,1] ranging from bosons (α = 0) to fermions (α = 1). We prove a (magnetic) Hardy inequality for anyons, which in the case that α is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by Dyson and Lenard’s original approach to the stability of fermionic matter in three dimensions, we prove a Lieb-Thirring inequality for these types of anyons.

Place, publisher, year, edition, pages
Springer, 2013
National Category
Mathematical Analysis Condensed Matter Physics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-179450 (URN)10.1007/s00220-013-1748-4 (DOI)000321957000008 ()2-s2.0-84880509717 (Scopus ID)
Note

QC 20160119

Available from: 2015-12-16 Created: 2015-12-16 Last updated: 2017-12-01Bibliographically approved
Lundholm, D. & Solovej, J. P. (2013). Local exclusion principle for identical particles obeying intermediate and fractional statistics. Physical Review A. Atomic, Molecular, and Optical Physics, 88(6), 062106
Open this publication in new window or tab >>Local exclusion principle for identical particles obeying intermediate and fractional statistics
2013 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 88, no 6, p. 062106-Article in journal (Refereed) Published
Abstract [en]

A local exclusion principle is observed for identical particles obeying intermediate and fractional exchange statistics in one and two dimensions, leading to bounds for the kinetic energy in terms of the density. This has implications for models of Lieb-Liniger and Calogero-Sutherland type and implies a nontrivial lower bound for the energy of the anyon gas whenever the statistics parameter is an odd numerator fraction. We discuss whether this is actually a necessary requirement.

Keywords
anyons, intermediate and fractional statistics, energy bounds, Lieb-Thirring inequalities, many-body quantum mechanics
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-138837 (URN)10.1103/PhysRevA.88.062106 (DOI)000328674600004 ()2-s2.0-84891691913 (Scopus ID)
Funder
EU, European Research Council, 321029
Note

QC 20140121

Available from: 2013-12-20 Created: 2013-12-20 Last updated: 2017-12-06Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-3456-5846

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