☆ 4.6 Article

Symmetries of three harmonically trapped particles in one dimension

PHYSICAL REVIEW A (2012)

Journal

PHYSICAL REVIEW A

Volume 86, Issue 5, Pages -

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AMER PHYSICAL SOC

DOI: 10.1103/PhysRevA.86.052122

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Optics Physics, Atomic, Molecular & Chemical

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Abstract

We present a method for solving few-body problems for trapped particles and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical coordinates, i.e., the two-dimensional version of three- body hyperspherical coordinates, we discover an underlying C-6v symmetry. This symmetry simplifies the calculation of energy eigenstates of the full Hamiltonian in a truncated Hilbert space constructed from the trap Hamiltonian eigenstates. Particle superselection rules are implemented by choosing the relevant representations of C-6v. We find that the one-dimensional system shows nearly the full richness of the three-dimensional system, and can be used to understand separability and reducibility in this system and in standard few-body approximation techniques.

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Padilla Aranda, G. Padovano, S. Pagan Griso, G. Palacino, A. Palazzo, S. Palazzo, S. Palestini, M. Palka, J. Pan, T. Pan, D. K. Panchal, C. E. Pandini, J. G. Panduro Vazquez, P. Pani, G. Panizzo, L. Paolozzi, C. Papadatos, S. Parajuli, A. Paramonov, C. Paraskevopoulos, D. Paredes Hernandez, T. H. Park, M. A. Parker, F. Parodi, E. W. Parrish, V. A. Parrish, J. A. Parsons, U. Parzefall, B. Pascual Dias, L. Pascual Dominguez, V. R. Pascuzzi, F. Pasquali, E. Pasqualucci, S. Passaggio, F. Pastore, P. Pasuwan, J. R. Pater, J. Patton, T. Pauly, J. Pearkes, M. Pedersen, R. Pedro, S. V. Peleganchuk, O. Penc, C. Peng, H. Peng, M. Penzin, B. S. Peralva, A. P. Pereira Peixoto, L. Pereira Sanchez, D. V. Perepelitsa, E. Perez Codina, M. Perganti, L. Perini, H. Pernegger, S. Perrella, A. Perrevoort, O. Perrin, K. Peters, R. F. Y. Peters, B. A. Petersen, T. C. Petersen, E. Petit, V. Petousis, C. Petridou, A. Petrukhin, M. Pettee, N. E. Pettersson, A. Petukhov, K. Petukhova, A. Peyaud, R. Pezoa, L. 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Queitsch-Maitland, G. Rabanal Bolanos, D. Rafanoharana, F. Ragusa, J. L. Rainbolt, J. A. Raine, S. Rajagopalan, E. Ramakoti, K. Ran, V. Raskina, D. F. Rassloff, S. Rave, B. Ravina, I. Ravinovich, M. Raymond, A. L. Read, N. P. Readioff, D. M. Rebuzzi, G. Redlinger, K. Reeves, J. A. Reidelsturz, D. Reikher, A. Reiss, A. Rej, C. Rembser, A. Renardi, M. Renda, M. B. Rendel, A. G. Rennie, S. Resconi, M. Ressegotti, D. Resseguie, S. Rettie, B. Reynolds, E. Reynolds, M. Rezaei Estabragh, O. L. Rezanova, P. Reznicek, E. Ricci, R. Richter, S. Richter, E. Richter-Was, M. Ridel, P. Rieck, P. Riedler, M. Rijssenbeek, A. Rimoldi, M. Rimoldi, L. Rinaldi, T. T. Rinn, M. P. Rinnagel, G. Ripellino, I. Riu, P. Rivadeneira, J. C. Rivera Vergara, F. Rizatdinova, E. Rizvi, C. Rizzi, B. A. Roberts, B. R. Roberts, S. H. Robertson, M. Robin, D. Robinson, C. M. Robles Gajardo, M. Robles Manzano, A. Robson, A. Rocchi, C. Roda, S. Rodriguez Bosca, Y. Rodriguez Garcia, A. Rodriguez Rodriguez, A. M. Rodriguez Vera, S. Roe, J. T. Roemer, A. R. Roepe-Gier, J. Roggel, O. Rhne, R. A. Rojas, B. Roland, C. P. A. Roland, J. Roloff, A. Romaniouk, E. Romano, M. Romano, A. C. Romero Hernandez, N. Rompotis, L. Roos, S. Rosati, J. Rosser, E. Rossi, E. Rossi, L. P. Rossi, L. Rossini, R. Rosten, M. Rotaru, B. Rottler, D. Rousseau, D. Rousso, G. Rovelli, A. Roy, A. Rozanov, Y. Rozen, X. Ruan, A. Rubio Jimenez, A. J. Ruby, T. A. Ruggeri, F. Ruehr, A. Ruiz-Martinez, A. Rummler, Z. Rurikova, N. A. Rusakovich, H. L. Russell, J. P. Rutherfoord, E. M. Ruettinger, K. Rybacki, M. Rybar, E. B. Rye, A. Ryzhov, J. A. Sabater Iglesias, P. Sabatini, L. Sabetta, H. F-W. Sadrozinski, F. Safai Tehrani, B. Safarzadeh Samani, M. Safdari, S. Saha, M. Sahinsoy, M. Saimpert, M. Saito, T. Saito, D. Salamani, G. Salamanna, A. Salnikov, J. Salt, A. Salvador Salas, D. Salvatore, F. Salvatore, A. Salzburger, D. Sammel, D. Sampsonidis, D. Sampsonidou, J. Sanchez, A. Sanchez Pineda, V. Sanchez Sebastian, H. Sandaker, C. O. Sander, J. A. Sandesara, M. Sandhoff, C. Sandoval, D. P. C. Sankey, A. Sansoni, L. Santi, C. Santoni, H. Santos, S. N. Santpur, A. Santra, K. A. Saoucha, J. G. Saraiva, J. Sardain, O. Sasaki, K. Sato, C. Sauer, F. Sauerburger, E. Sauvan, P. Savard, R. Sawada, C. Sawyer, L. Sawyer, I. Sayago Galvan, C. Sbarra, A. Sbrizzi, T. Scanlon, J. Schaarschmidt, P. Schacht, D. Schaefer, U. Schaefer, A. C. Schaffer, D. Schaile, R. D. Schamberger, E. Schanet, C. Scharf, V. A. Schegelsky, D. Scheirich, F. Schenck, M. Schernau, C. Scheulen, C. Schiavi, Z. M. Schillaci, E. J. Schioppa, M. Schioppa, B. Schlag, K. E. Schleicher, S. Schlenker, K. Schmieden, C. Schmitt, S. Schmitt, L. Schoeffel, A. Schoening, P. G. Scholer, E. Schopf, M. Schott, J. Schovancova, S. Schramm, F. Schroeder, H-C. Schultz-Coulon, M. Schumacher, B. A. Schumm, Ph. Schune, A. Schwartzman, T. A. Schwarz, Ph. Schwemling, R. Schwienhorst, T. A. Sciandra, G. Sciolla, F. Scuri, F. Scutti, C. D. Sebastiani, K. Sedlaczek, P. Seema, S. C. Seidel, A. Seiden, B. D. Seidlitz, T. Seiss, C. Seitz, J. M. Seixas, G. Sekhniaidze, S. J. Sekula, L. Selem, N. Semprini-Cesari, S. Sen, D. Sengupta, V. Senthilkumar, L. Serin, L. Serkin, M. Sessa, H. Severini, S. Sevova, F. Sforza, A. Sfyrla, E. Shabalina, R. Shaheen, J. D. Shahinian, N. W. Shaikh, D. Shaked Renous, L. Y. Shan, M. Shapiro, A. Sharma, A. S. Sharma, P. Sharma, S. Sharma, P. B. Shatalov, K. Shaw, S. M. Shaw, Q. Shen, P. Sherwood, L. Shi, C. O. Shimmin, Y. Shimogama, J. D. Shinner, I. P. J. Shipsey, S. Shirabe, M. Shiyakova, J. Shlomi, M. J. Shochet, J. Shojaii, D. R. Shope, S. Shrestha, E. M. Shrif, ,

Summary: Constraints on the Higgs boson self-coupling are determined by combining double-Higgs boson analyses and single-Higgs boson analyses. The combination of the double-Higgs analyses sets an upper limit on the double-Higgs production cross-section. By combining the single-Higgs and double-Higgs analyses, values outside a certain interval are excluded at a certain confidence level.

PHYSICS LETTERS B (2023)

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Article Physics, Condensed Matter

Artificial magnetism for a harmonically trapped Fermi gas in a synthetic magnetic field

Shyamal Biswas, Avijit Ghosh, Soumyadeep Majumder

Summary: We have analytically explored the effects of a synthetic magnetic field on a 3D spin-polarized trapped Fermi gas of electrically neutral particles. While spin polarization is necessary for trapping neutral atoms in a magneto-optical trap, the study of Pauli paramagnetism is not possible for a spin-polarized Fermi system. However, we can study Landau diamagnetism and de Haas-van Alphen effect for this system. Our unified framework allows for the study of these effects at all temperatures and magnitudes of the synthetic magnetic field in the thermodynamic limit. This prediction can be tested using current experimental setups for ultracold fermionic atoms in magneto-optical traps.

JOURNAL OF PHYSICS-CONDENSED MATTER (2023)

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Article Physics, Applied

Dynamic vortex evolution of harmonically trapped coupled Bose-Einstein condensate with quintic nonlinearity

Yunsong Guo, Yubin Jiao, Xiaoning Liu, Xiangbo Zhu, Ying Wang

Summary: This study investigates the evolution of vortex in harmonically trapped two-component coupled Bose-Einstein condensate with quintic-order nonlinearity. The vortex solution of this two-component system is derived based on the coupled quintic-order Gross-Pitaevskii equation model and the variational method. It is found that the evolution of vortex is a metastable state.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B (2022)

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Article Physics, Multidisciplinary

Impurities in systems of noninteracting trapped fermions

David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr

Summary: The study focuses on the properties of spin-less non-interacting fermions trapped in a one-dimensional confining potential with one or more impurities modeled by delta function potentials. The method based on the single particle Green's function is employed to calculate the effects of impurities on the Fermi gas density and the effective potential. Results show interesting transitions and modifications in the density and potential when impurities are placed at different locations, such as near the edge of the trap or in the bulk.

SCIPOST PHYSICS (2021)

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Article Physics, Multidisciplinary

One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries. II. N Particles

N. L. Harshman

FEW-BODY SYSTEMS (2016)

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Article Physics, Multidisciplinary

One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles

N. L. Harshman

FEW-BODY SYSTEMS (2016)

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Article Physics, Multidisciplinary

Identical Wells, Symmetry Breaking, and the Near-Unitary Limit

N. L. Harshman

FEW-BODY SYSTEMS (2017)

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Article Physics, Multidisciplinary

Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

N. L. Harshman, Maxim Olshanii, A. S. Dehkharghani, A. G. Volosniev, Steven Glenn Jackson, N. T. Zinner

PHYSICAL REVIEW X (2017)

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Article Physics, Multidisciplinary

Coincidence Structures and Hard-Core Few-Body Interactions

N. L. Harshman, A. C. Knapp

FEW-BODY SYSTEMS (2018)

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Article Optics

Spectroscopy for a few atoms harmonically trapped in one dimension

N. L. Harshman

PHYSICAL REVIEW A (2014)

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Article Physics, Multidisciplinary

Anyons from three-body hard-core interactions in one dimension

N. L. Harshman, A. C. Knapp

ANNALS OF PHYSICS (2020)

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Article Mathematics

The Dynamics of Digits: Calculating Pi with Galperin's Billiards

Xabier M. Aretxabaleta, Marina Gonchenko, Nathan L. Harshman, Steven Glenn Jackson, Maxim Olshanii, Grigory E. Astrakharchik

MATHEMATICS (2020)

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Article Quantum Science & Technology

Probing the edge between integrability and quantum chaos in interacting few-atom systems

Thomas Fogarty, Miguel Angel Garcia-March, Lea F. Santos, N. L. Harshman

Summary: The study proposes a minimal chaos model that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials, investigating the emergence of chaos as the number of particles and wells increases. It reveals a narrow boundary between integrability and chaos in a highly tunable few-body system, showing subtle indications of quantum chaos for 3 particles and stronger signatures for 4 particles. The analysis is performed for bosonic particles and has the potential to be extended to distinguishable fermions.

QUANTUM (2021)

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Article Optics

Topological exchange statistics in one dimension

N. L. Harshman, A. C. Knapp

Summary: The standard topological approach is limited in analyzing exchange statistics of indistinguishable particles in one dimension. By including path-ambiguous singular points and considering configuration space as an orbifold, a unified analysis of exchange statistics in any dimension becomes possible, predicting the existence of non-Abelian anyons in one-dimensional systems.

PHYSICAL REVIEW A (2022)

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Article Quantum Science & Technology

Graded-index optical fiber emulator of an interacting three-atom system: illumination control of particle statistics and classical non-separability

M. A. Garcia-March, N. L. Harshman, H. Silva, T. Fogarty, Th Busch, M. Lewenstein, A. Ferrando

QUANTUM (2019)

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Article Optics

Hybrid model of separable, zero-range, few-body interactions in one-dimensional harmonic traps

Molte Emil Strange Andersen, N. L. Harshman, Nikolaj Thomas Zinner

PHYSICAL REVIEW A (2017)

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Article Optics

Infinite barriers and symmetries for a few trapped particles in one dimension

N. L. Harshman

PHYSICAL REVIEW A (2017)

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Proceedings Paper Physics, Nuclear

Five is More: Comments on Symmetry, Integrability, and Solvability for a Few Particles in a One-Dimensional Trap

N. L. Harshman

21ST INTERNATIONAL CONFERENCE ON FEW-BODY PROBLEMS IN PHYSICS (2016)

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Article Physics, Multidisciplinary

A solvable model for decoupling of interacting clusters

Artem G. Volosniev, Aksel S. Jensen, Nathan L. Harshman, Jeremy R. Armstrong, Nikolaj T. Zinner

EPL (2019)

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