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Lundholm, Douglasorcid.org/0000-0003-3456-5846

Open this publication in new window or tab >>Fermionic behavior of ideal anyons### Lundholm, Douglas

### Seiringer, Robert

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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#####

##### Funder

Swedish Research Council, 2013-4734EU, Horizon 2020, 694227
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

IST Austria, Campus 1, A-3400 Klosterneuburg, Austria..

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.

QC 20181022

Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2018-10-24Bibliographically approvedOpen this publication in new window or tab >>Local density approximation for almost-bosonic anyons### Correggi, M.

### Lundholm, Douglas

### Rougerie, N.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 717, p. 77-92Article in journal (Refereed) Published
##### Abstract [en]

##### 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)
#####

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#####

##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20190321

Available from: 2019-03-21 Created: 2019-03-21 Last updated: 2019-10-18Bibliographically approvedOpen this publication in new window or tab >>Emergence of Fractional Statistics for Tracer Particles in a Laughlin Liquid### Lundholm, Douglas

### Rougerie, Nicolas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_j_idt371",{id:"formSmash:j_idt184:2:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_j_idt371",multiple:true});
#####

##### Projects

VR 2013-4734: Spectral theory of quantum systems with exotic symmetries
##### Funder

Swedish Research Council, 2013-4734
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

LPMMC (UMR 5493), Université Grenoble-Alpes and CNRS.

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.

QC 20160503

Available from: 2016-04-29 Created: 2016-04-29 Last updated: 2017-11-30Bibliographically approvedOpen this publication in new window or tab >>Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems### Lundholm, Douglas

### Nam, Phan Thành

### Portmann, Fabian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt371",{id:"formSmash:j_idt184:3:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt371",multiple:true});
#####

##### 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

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20160220

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approvedOpen this publication in new window or tab >>Geometric extensions of many-particle Hardy inequalities### Lundholm, Douglas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20150518

Available from: 2015-04-12 Created: 2015-04-12 Last updated: 2017-12-04Bibliographically approvedOpen this publication in new window or tab >>Lieb-Thirring Bounds for Interacting Bose Gases### Lundholm, Douglas

### Portmann, Fabian

### Solovej, Jan Philip

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Funder

Knut and Alice Wallenberg Foundation, KAW 2010.0063Swedish Research Council, 2013-4734 2012-3864EU, European Research Council, 321029
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

University of Copenhagen, Denmark.

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.

QC 20150408. Updated from manuscript to article in journal.

Available from: 2014-05-07 Created: 2014-05-07 Last updated: 2017-12-05Bibliographically approvedOpen this publication in new window or tab >>The Average Field Approximation for Almost Bosonic Extended Anyons### Lundholm, Douglas

### Rougerie, Nicolas

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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#####

##### 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

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

CNRS & LPMMC Grenoble.

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.

QC 20151218

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approvedOpen this publication in new window or tab >>Local Exclusion and Lieb-Thirring Inequalities for Intermediate and Fractional Statistics### Lundholm, Douglas

### Solovej, Jan Philip

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Note

Institut Mittag-Leffler.

University of Copenhagen.

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.

QC 20160119

Available from: 2015-12-16 Created: 2015-12-16 Last updated: 2017-12-01Bibliographically approvedOpen this publication in new window or tab >>Hardy and Lieb-Thirring Inequalities for Anyons### Lundholm, Douglas

### Solovej, Jan Philip

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Note

University of Copenhagen.

University of Copenhagen.

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.

QC 20160119

Available from: 2015-12-16 Created: 2015-12-16 Last updated: 2017-12-01Bibliographically approvedOpen this publication in new window or tab >>Local exclusion principle for identical particles obeying intermediate and fractional statistics### Lundholm, Douglas

### Solovej, Jan Philip

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##### Abstract [en]

##### 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)
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##### Funder

EU, European Research Council, 321029
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

University of Copenhagen.

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.

QC 20140121

Available from: 2013-12-20 Created: 2013-12-20 Last updated: 2017-12-06Bibliographically approved