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Journal articles on the topic 'Landau lowest level equation'

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Published: 12 October 2024

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1

Gérard, Patrick, Pierre Germain, and Laurent Thomann. "On the Cubic Lowest Landau Level Equation." Archive for Rational Mechanics and Analysis 231, no. 2 (August 16, 2018): 1073–128. http://dx.doi.org/10.1007/s00205-018-1295-4.

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2

Sheng, Dong-Ning, Zhao-Bin Su, and B. Sakita. "On the Constraint Equation for the Lowest Landau Level in Fractional Quantum Hall System." International Journal of Modern Physics B 05, no. 10 (June 1991): 1715–24. http://dx.doi.org/10.1142/s0217979291001619.

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In the framework of collective field theory, We apply the Chern-Simon field theory treatment to the constraint equation for the lowest Landau level to investigate the generic properties for the quasi-particles of the FQH system. It shows a transparent connection to the Laughlin's wave functions. If we take an average over the wave functional for the constraint equation, the resulted equation can be interpreted as the vortex equation for the fractionally charged quasi-particles. Introducing a generalized ρ (density)-ϑ (phase) transformation, not only the fractional statistics and the hierarchy scheme can be drawn from the constraint equation, it also gives rise an interesting picture that vortices condense as a Halperin like wave fuction on a Laughlin like background condensate of ν=1/m.

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3

Sakita, B., Dong-Ning Sheng, and Zhao-Bin Su. "Constraint equation for the lowest Landau level in the fractional quantum Hall system." Physical Review B 44, no. 20 (November 15, 1991): 11510–13. http://dx.doi.org/10.1103/physrevb.44.11510.

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4

Mashkevich, Stefan, and Stéphane Ouvry. "The lowest Landau level anyon equation of state in the anti-screening regime." Physics Letters A 310, no. 2-3 (April 2003): 85–94. http://dx.doi.org/10.1016/s0375-9601(03)00261-5.

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5

Schwinte, Valentin, and Laurent Thomann. "Growth of Sobolev norms for coupled lowest Landau level equations." Pure and Applied Analysis 3, no. 1 (May 28, 2021): 189–222. http://dx.doi.org/10.2140/paa.2021.3.189.

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6

MYUNG, YUN SOO. "CHIRAL BOSON, CHIRAL VACUUM AND EDGE STATES IN THE FRACTIONAL QUANTUM HALL EFFECT." International Journal of Modern Physics A 09, no. 07 (March 20, 1994): 1181–95. http://dx.doi.org/10.1142/s0217751x94000546.

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By performing the Gupta–Bleuler quantization of a chiral boson, we obtain the chiral constraints, which correspond to the lowest Landau level conditions. From these, the chiral vacuum is defined as the vacuum of admixtures of many-harmonic oscillators. We construct the wave function for edge states of a droplet of incompressible quantum Hall fluid, by solving Schrödinger's equation on the basis of the chiral vacuum. This bosonic function can describe the collective edge modes, which are fundamentally a many-body effect of fermions at the lowest Landau level. In detail, the neutral edge state of FQHE is described by the α = 1 chiral boson theory. The charged edge states are described by the α ≠ 1 chiral boson theory.

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7

RAJARAMAN, R. "CURRENTS IN THE LOWEST LANDAU LEVEL FIELD THEORY WITH e–e INTERACTIONS." International Journal of Modern Physics B 08, no. 06 (March 15, 1994): 777–88. http://dx.doi.org/10.1142/s0217979294000312.

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We obtain expressions for the electric current in the Lowest Landau Level field theory in the presence of a general (external as well as inter-particle) interaction. This is done in the constrained Lagrangian formulation and is an extension of results obtained by Martinez and Stone for the external force case. However, we work directly with nonlocal field equations rather than convert the Lagrangian into a local one and use Noether's theorem.

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8

Ćirić, Marija Dimitrijević, and Nikola Konjik. "Landau levels from noncommutative U(1)⋆ gauge theory in κ-Minkowski space-time." International Journal of Geometric Methods in Modern Physics 15, no. 08 (June 22, 2018): 1850141. http://dx.doi.org/10.1142/s0219887818501414.

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Motivated by physics of the Lowest Landau Level and the Quantum Hall Effect, we investigate motion of an electron in a constant background magnetic field in the [Formula: see text]-Minkowski space-time. Starting from an action invariant under the noncommutative [Formula: see text] gauge transformations, we obtain the [Formula: see text]-deformed Dirac equation. Using the perturbative approach, we calculate noncommutative corrections to energy levels, mass and the gyromagnetic ratio up to the first order in the deformation parameter [Formula: see text].

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9

Sakita, B., Dong-Ning Sheng, and Zhao-Bin Su. "COLLECTIVE FIELD THEORY APPLIED TO THE FRACTIONAL QUANTUM HALL EFFECT." International Journal of Modern Physics B 05, no. 01n02 (January 1991): 417–26. http://dx.doi.org/10.1142/s0217979291000262.

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We present an application of collective field theory to the fractional quantum Hall effect (FQHE). We first express the condition, that the electrons are all in the lowest Landau level, as a constraint equation for the state functional. We then derive the fractional filling factor from this equation together with the no-free-vortex assumption. A hierarchy of filling factors is derived by using the particle-vortex dual transformations. In the final section we discuss an attempt at a dynamical theory of FQHE, which would justify the no-free-vortex assumption. A derivation of Laughlin’s wave function with and without quasi-hole excitations is also given.

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10

PEREZ MARTINEZ, A., and A. CABO. "HARTREE-FOCK APPROXIMATION FOR COULOMB INTERACTING ANYON GAS IN A MAGNETIC FIELD." Modern Physics Letters B 05, no. 24n25 (October 1991): 1703–12. http://dx.doi.org/10.1142/s0217984991002057.

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Dyson equations for a Coulomb interacting anyon gas in a magnetic field are obtained and solved in the Hartree-Fock approximation. The states recently proposed by Greiter and Wilczek naturally arise from the Hartree-Fock solution. The electron self energies are calculated in the case when only the lowest Landau level is occupied.

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11

Parle, AJ. "Quantum Electrodynamics in Strong Magnetic Fields. IV. Electron Self-energy." Australian Journal of Physics 40, no. 1 (1987): 1. http://dx.doi.org/10.1071/ph870001.

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The electron self-energy in a magnetic field is calculated with the effect of the field included exactly. A new representation of the wavefunctions and other quantities is defined, in which the mass operator has a particularly simple form. After renormalisation, the form of the mass operator allows corrections to the Dirac equation, wavefunctions, vertex function and the electron propagator close to the mass shell to be calculated to lowest order in the fine structure constant. The probability for an electron to change spin while remaining in the same Landau level is calculated, and is found to be much less than the probability of cyclotron emission.

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12

FERRARI, R. "FRACTIONAL QUANTUM HALL EFFECT: CONSTRUCTION OF THE HARTREE–FOCK STATE BY USING TRANSLATIONAL COVARIANCE." International Journal of Modern Physics B 08, no. 05 (February 28, 1994): 529–79. http://dx.doi.org/10.1142/s0217979294000221.

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The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the Coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations (up to a gauge transformation). This paper is devoted to the case of low filling factor, thus we limit ourselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor νf = 1/u we give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree–Fock equation. For general filling factor νf = u′/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. We generalize the Hartree–Fock equation by considering some correlation: all quantum states are allowed for the u′ electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (νf = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). Our results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed.

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13

Chamel, Nicolas, and Anthea Francesca Fantina. "Onset of Electron Captures and Shallow Heating in Magnetars." Universe 8, no. 6 (June 11, 2022): 328. http://dx.doi.org/10.3390/universe8060328.

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The loss of magnetic pressure accompanying the decay of the magnetic field in a magnetar may trigger exothermic electron captures by nuclei in the shallow layers of the stellar crust. Very accurate analytical formulas are obtained for the threshold density and pressure, as well as for the maximum amount of heat that can be possibly released, taking into account the Landau–Rabi quantization of electron motion. These formulas are valid for arbitrary magnetic field strengths, from the weakly quantizing regime to the most extreme situation in which electrons are all confined to the lowest level. Numerical results are also presented based on experimental nuclear data supplemented with predictions from the Brussels-Montreal model HFB-24. This same nuclear model has been already employed to calculate the equation of state in all regions of magnetars.

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14

RAJARAMAN, R., and S. L. SONDHI. "A FIELD THEORY FOR THE READ OPERATOR." International Journal of Modern Physics B 10, no. 07 (March 30, 1996): 793–803. http://dx.doi.org/10.1142/s0217979296000337.

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We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Read's original work we do not work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our bosonic field operators. We describe a Lagrangian formalism, derive the equations of motion for the fields and present a family of mean-field solutions. Finally, we show that these mean field solutions are precisely the Laughlin states. We do not, in this work, address the treatment of fluctuations.

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15

Adorno, Tiago C., Dmitry M. Gitman, and Anatoly E. Shabad. "Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field." Universe 6, no. 11 (November 5, 2020): 204. http://dx.doi.org/10.3390/universe6110204.

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We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

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16

RAJARAMAN, R., and S. L. SONDHI. "LANDAU LEVEL MIXING AND SOLENOIDAL TERMS IN LOWEST LANDAU LEVEL CURRENTS." Modern Physics Letters B 08, no. 17 (July 20, 1994): 1065–73. http://dx.doi.org/10.1142/s0217984994001072.

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We calculate the lowest Landau level (LLL) current by working in the full Hilbert space of a two-dimensional electron system in a magnetic field and keeping all the nonvanishing terms in the high field limit. The answer i) is not represented by a simple LLL operator and ii) differs from the current operator, recently derived by Martinez and Stone in a field theoretic LLL formalism, by solenoidal terms. Though that is consistent with the inevitable ambiguities of their Noether construction, we argue that the correct answer cannot arise naturally in the LLL formalism.

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17

Bruckmann, Falk, Gergely Endrődi, Matteo Giordano, Sándor D. Katz, Tamás G. Kovács, Ferenc Pittler, and Jacob Wellnhofer. "The lowest Landau level in QCD." EPJ Web of Conferences 137 (2017): 03003. http://dx.doi.org/10.1051/epjconf/201713703003.

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18

Yomba, Emmanuel, and Timoléon Crépin Kofané. "Solutions of the Lowest Order Complex Ginzburg-Landau Equation." Journal of the Physical Society of Japan 69, no. 4 (April 15, 2000): 1027–32. http://dx.doi.org/10.1143/jpsj.69.1027.

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19

Fletcher, Richard J., Airlia Shaffer, Cedric C. Wilson, Parth B. Patel, Zhenjie Yan, Valentin Crépel, Biswaroop Mukherjee, and Martin W. Zwierlein. "Geometric squeezing into the lowest Landau level." Science 372, no. 6548 (June 17, 2021): 1318–22. http://dx.doi.org/10.1126/science.aba7202.

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The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits’ centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.

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20

Huo, Y., R. E. Hetzel, and R. N. Bhatt. "Universal conductance in the lowest Landau level." Physical Review Letters 70, no. 4 (January 25, 1993): 481–84. http://dx.doi.org/10.1103/physrevlett.70.481.

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21

Klevtsov, S. "Bergman kernel from the lowest Landau level." Nuclear Physics B - Proceedings Supplements 192-193 (July 2009): 154–55. http://dx.doi.org/10.1016/j.nuclphysbps.2009.07.063.

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22

Hatsuda, Machiko, Satoshi Iso, and Hiroshi Umetsu. "Noncommutative superspace, supermatrix and lowest Landau level." Nuclear Physics B 671 (November 2003): 217–42. http://dx.doi.org/10.1016/j.nuclphysb.2003.08.013.

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23

Salem-Sugui, Said, M. Friesen, A. D. Alvarenga, Osvaldo F. Schilling, F. G. Gandra, and M. M. Doria. "Lowest Landau level diamagnetic fluctuations in niobium." Physica C: Superconductivity 408-410 (August 2004): 664–65. http://dx.doi.org/10.1016/j.physc.2004.06.010.

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24

MARTÍNEZ, JUAN, and MICHAEL STONE. "CURRENT OPERATORS IN THE LOWEST LANDAU LEVEL." International Journal of Modern Physics B 07, no. 26 (November 30, 1993): 4389–401. http://dx.doi.org/10.1142/s0217979293003723.

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We use Noether’s theorem to generate a consistent definition of the current operator for electrons restricted to the lowest Landau level. We exhibit the connection between this current and the Moyal bracket, or W∞, algebra, and use it to derive the edge-charge algebra for the ν=1/(2n+1) FQHE states.

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25

Shibata, Naokazu, and Daijiro Yoshioka. "Stripe State in the Lowest Landau Level." Journal of the Physical Society of Japan 73, no. 1 (January 15, 2004): 1–4. http://dx.doi.org/10.1143/jpsj.73.1.

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26

Hofmann, Johannes, and Wilhelm Zwerger. "Scale Invariance in the Lowest Landau Level." Comptes Rendus. Physique 24, S3 (June 13, 2023): 1–18. http://dx.doi.org/10.5802/crphys.137.

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27

Abidin, Zainal, Syarifuddin Kadir, and Eko Rini Indriyatie. "ANALISIS TINGKAT BAHAYA EROSI DARI VEGETASI ALANG-ALANG PADA BERBAGAI KELERENGAN DI SUB DAS BATI-BATI (DAS MALUKA) KALIMANTAN SELATAN." Jurnal Sylva Scienteae 5, no. 5 (October 31, 2022): 718. http://dx.doi.org/10.20527/jss.v5i5.6694.

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The type of land cover affects the level of erosion hazard in an area. The purpose of this study was to analyze the amount of erosion hazard and determine the level of erosion hazard (TBE) on the reed vegetation on various slopes in the Bati-bati sub-watershed of the Maluka watershed, South Kalimantan. Sampling of data using purposive sampling technique. Samples were taken as many as 6 land units based on vegetation, soil type, reed land cover and slope class, which were obtained from the map overlay of land units. Each sample point was taken soil samples using a sample ring to be tested in the laboratory. Then, the data were analyzed using Universal Soil Loss Equation (USLE) and Erosion Hazard Analysis (TBE). The highest number of erosion values occurred in reed Land Unit (UL) 39 with a slope of 15-25% with an erosion value of 130.96 tons/ha/year, while the lowest erosion value was found in UL 34 with a slope of 0-8 and erosion of 9.64 tons/ha/year. The erosion hazard level of the land unit under study shows the percentage of light grade (IR) occurring at UL7, UL 34, UL 50 and UL 59 with a flat slope (0-8), while the medium grade (II-S) occurs at UL. 37 with gentle slopes (8-15) and UL 39 with steep slopes (25-40)Jenis penutupan lahan berpengaruh terhadap tingkat bahaya erosi dalam suatu wilayah. Tujuan dari penelitian ini ialah menganalisis jumlah bahaya erosi dan menentukan adanya tingkat bahaya erosi (TBE) pada vegetasi alang-alang pada berbagai kelerengan di sub DAS Bati-bati DAS Maluka, Kalimantan Selatan. Pengambilan sampel data menggunakan teknik purposive sampling. Sampel diambil sebanyak 6 unit lahan berdasarkan vegetasi, jenis tanah, tutupan lahan alang-alang dan kelas kelerengan, yang didapat dari overlay peta satuan lahan. Setiap titik sampel diambil sampel tanahnya menggunakan ring sampel untuk diuji di laboratorium. Kemudian, data dianalisis menggunakan persamaan Universal Soil Loss Equation (USLE) dan Analisis Tingkat Bahaya Erosi (TBE). Jumlah nilai erosi tertinggi terjadi pada Unit Lahan Alang-Alang (UL) 39 dengan kemiringan lereng 15-25% dengan nilai erosi sebesar130,96 ton/ha/thn, sedangkan nilai erosi terendah terdapat pada UL 34 dengan kemiringan lereng 0-8 dan nilai erosi sebesar 9,64 ton/ha/thn. Tingkat bahaya erosi dari unit lahan yang diteliti menunjukkan persentase kelas ringan (I-R) terjadi pada UL7, UL 34, UL 50 dan UL 59 dengan kemiringan lereng yang datar (0-8), sedangkan pada kelas sedang (II-S) terjadi pada UL 37 dengan kemiringan lereng landai (8-15) dan UL 39 dengan kemiringan lereng curam (25-40).

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28

Avishai, Yshai, and Richard Berkovits. "Distribution of level curvatures in the lowest Landau level." Physical Review B 55, no. 12 (March 15, 1997): 7791–95. http://dx.doi.org/10.1103/physrevb.55.7791.

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29

Pambudi, Andi Setyo. "Environmental land use conflicts and ecosystem services: a paper review." Indonesian Journal of Applied Environmental Studies 4, no. 2 (October 29, 2023): 58–63. http://dx.doi.org/10.33751/injast.v4i2.7851.

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The topic of potential conflicts related to land use involving human activities in a watershed is an important matter to be discussed. The background of this research is that conditions in mountainous watersheds, and agricultural land use cause changes in ecosystem services, with trade-offs between crop production and erosion regulation. Watershed management with an environmental concept often faces problems with different interests among stakeholders. Although several studies have initiated the mapping of land-use conflicts between human activities and conservation, the spatial assessment of land-use conflicts on environmental issues and trade-offs of ecosystem services in agricultural areas has not been fully considered. The purpose of this study is to map land use, with indicators of measuring conflicts in the value of conservation and agricultural development, through scenarios of the level of erosion hazard on agricultural land. This study provides input to decision-makers regarding watershed conservation efforts that still consider aspects of the economic needs of agricultural land. The objective of the reviewers is to understand how the concept of mapping the potential conflict of land use in the Haean watershed in South Korea can be applied in Indonesia. The methodology used is to apply the agricultural land suitability index based on various analytical criteria to estimate the spatial preferences of agricultural activities. To predict erosion, using the Revised Universal Soil Loss Equation (RUSLE) method and the classification of agricultural land in the watershed is divided into four levels of land use conflict (lowest, low, high, and highest).

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30

Huo, Y., and R. N. Bhatt. "Current carrying states in the lowest Landau level." Physical Review Letters 68, no. 9 (March 2, 1992): 1375–78. http://dx.doi.org/10.1103/physrevlett.68.1375.

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31

Pierson, Stephen W., and Oriol T. Valls. "Flux-lattice melting and lowest-Landau-level fluctuations." Physical Review B 57, no. 14 (April 1, 1998): R8143—R8145. http://dx.doi.org/10.1103/physrevb.57.r8143.

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32

Melik-Alaverdian, V., N. E. Bonesteel, and G. Ortiz. "Skyrmion physics beyond the lowest Landau-level approximation." Physical Review B 60, no. 12 (September 15, 1999): R8501—R8504. http://dx.doi.org/10.1103/physrevb.60.r8501.

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33

Devitt, A. M., S. H. Roshko, U. Zeitler, C. J. Mellor, A. J. Kent, K. A. Benedict, T. Cheng, and M. Henini. "Ballistic phonon studies in the lowest Landau level." Physica E: Low-dimensional Systems and Nanostructures 6, no. 1-4 (February 2000): 47–51. http://dx.doi.org/10.1016/s1386-9477(99)00092-2.

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34

Sakita, B. "Symmetries of fermions in the lowest Landau level." Nuclear Physics B - Proceedings Supplements 101, no. 1-3 (August 2001): 70–80. http://dx.doi.org/10.1016/s0920-5632(01)01494-3.

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35

BAZZALI, D., and T. T. TRUONG. "COMPUTATION OF ENERGIES IN THE LOWEST LANDAU LEVEL." International Journal of Modern Physics B 15, no. 01 (January 10, 2001): 37–70. http://dx.doi.org/10.1142/s021797920100231x.

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We propose a novel calculation scheme to obtain various relevant energies in the Fractional Quantum Hall Effect for Ne charged particles confined to a disk interacting through Coulomb repulsion and with an uniform neutralizing background in the Lowest Landau Level. Numerical values for small Ne are compared to values obtained by Monte Carlo simulations or exact numerical diagonalizations. They are found to be remarkably close to each other, for different filling factors when the Laughlin wave function is used.

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36

Andreev, A. V. "Triplet superconductive pairing in the lowest Landau level." Physica C: Superconductivity 213, no. 3-4 (August 1993): 394–98. http://dx.doi.org/10.1016/0921-4534(93)90458-3.

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37

Manolescu, Andrei. "Static dielectric susceptibility of the lowest Landau level." Physical Review B 46, no. 4 (July 15, 1992): 2201–7. http://dx.doi.org/10.1103/physrevb.46.2201.

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38

MYUNG, YUN SOO. "W∞-ALGEBRA FOR FERMIONS IN THE LOWEST LANDAU LEVEL." Modern Physics Letters A 09, no. 06 (February 28, 1994): 549–55. http://dx.doi.org/10.1142/s0217732394003786.

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We derive the W∞-algebra directly from the cocycle (translational) transformation of fermions in the lowest Landau level. This happens whenever the translational symmetry is unbroken in the ground state. Under the cocycle transformations, the lowest Landau level condition and fermion number are preserved. In the droplet approximation, the algebra of this system is reduced to the classical w∞-algebra (area-preserving deformations) and is related to condensed matter physics. This describes the edge modes of the fractional quantum Hall effect.

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39

Bruckmann, Falk, Gergely Endrődi, Matteo Giordano, Sándor D. Katz, Tamás G. Kovács, Ferenc Pittler, and Jacob Wellnhofer. "Landau levels in QCD in an external magnetic field." EPJ Web of Conferences 175 (2018): 07014. http://dx.doi.org/10.1051/epjconf/201817507014.

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We will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. We will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, we will then show how one can define a “plowest Landau level” in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.

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40

MINE, TAKUYA, and YUJI NOMURA. "PERIODIC AHARONOV–BOHM SOLENOIDS IN A CONSTANT MAGNETIC FIELD." Reviews in Mathematical Physics 18, no. 08 (September 2006): 913–34. http://dx.doi.org/10.1142/s0129055x06002826.

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We consider the magnetic Schrödinger operator on R2. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. This condition is also necessary for the lowest Landau level. In the threshold case, we see that the spectrum near the lowest Landau level is purely absolutely continuous. Moreover, we shall give an estimate for the density of states for Landau levels and their gaps. The proof is based on the method of Geyler and Šťovíček, the magnetic Bloch theory, and canonical commutation relations.

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41

CHEN, YI-XIN, ZHONG-SHUI MA, and ZHAO-BIN SU. "W INFINITE SYMMETRIES IN THE HIERARCHICAL QUASIPARTICLE STATES (LOWEST LANDAU LEVEL STATES) OF THE FRACTIONAL QUANTUM HALL SYSTEMS." International Journal of Modern Physics B 09, no. 02 (January 20, 1995): 195–219. http://dx.doi.org/10.1142/s0217979295000112.

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We investigate the W infinite symmetries in the theory of general fractional quantum Hall effects by using the lowest Landau level constraint approach. We find that there does exist a W infinite symmetric algebra for the fractional quantum Hall system with all the quasiparticles being restricted to the lowest Landau level. The corresponding generators can be used to generate the new degenerate wavefunctions of the lowest Landau level states by means of Laughlin and Halperin wavefunctions. Meanwhile, we find there still exists another W infinite symmetric algebra in the system, whose generators are used to generate the degenerate wavefunctions of the lowest Landau level for the anti-quasiparticles. We conclude that the FQH system can effectively be described by quasiparticle features or anti-quasiparticle features. We also show that the local part of the W infinite symmetric algebras is the magnetic translation operator of the general fractional quantum Hall system. We finally construct the operators of the single mode wave density excitations in the system and discuss their operator product relations.

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42

LIU, DONGZI, and S. DAS SARMA. "UNIVERSALITY IN TWO–DIMENSIONAL LANDAU LEVEL LOCALIZATION." Modern Physics Letters B 07, no. 07 (March 20, 1993): 449–57. http://dx.doi.org/10.1142/s0217984993000448.

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We show, based on a direct numerical calculation of the Lyapunov exponents of the system and a finite-size single parameter scaling analysis, that the strong-field Landau level localization in a disordered two-dimensional electron gas is non-universal for short-range delta function random scatterers in the sense that the critical exponents in the two lowest Landau levels are substantially different. Inclusion of Landau level coupling and/or consideration of finite range of the random scattering potential in the theory restore the universality and make the computed critical exponents approximately equal.

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43

ELIASHVILI, M., and G. TSITSISHVILI. "GEOMETRIC TRANSFORMATIONS AND NCCS THEORY IN THE LOWEST LANDAU LEVEL." International Journal of Modern Physics B 16, no. 25 (October 10, 2002): 3725–36. http://dx.doi.org/10.1142/s0217979202014796.

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Chern-Simons type gauge field is generated by the means of singular area preserving transformations in the lowest Landau level of electrons forming fractional quantum Hall state. Dynamics is governed by the system of constraints which correspond to the Gauss law in the non-commutative Chern-Simons gauge theory and to the lowest Landau level condition in the picture of composite fermions. Physically reasonable solution to this constraints corresponds to the Laughlin state. It is argued that the model leads to the non-commutative Chern-Simons theory of the QHE and composite fermions.

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44

Jain, J. K., and R. K. Kamilla. "Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level." International Journal of Modern Physics B 11, no. 22 (September 10, 1997): 2621–60. http://dx.doi.org/10.1142/s0217979297001301.

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Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

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45

Moloni, Katerina, Mark Friesen, Shi Li, Victor Souw, P. Metcalf, Lifang Hou, and M. McElfresh. "3DXYand Lowest Landau Level Fluctuations in DeoxygenatedYBa2Cu3O7−δThin Films." Physical Review Letters 78, no. 16 (April 21, 1997): 3173–76. http://dx.doi.org/10.1103/physrevlett.78.3173.

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46

Li, Dingping, and Baruch Rosenstein. "Lowest Landau level approximation in strongly type-II superconductors." Physical Review B 60, no. 13 (October 1, 1999): 9704–13. http://dx.doi.org/10.1103/physrevb.60.9704.

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47

Antoine, J. P., and F. Bagarello. "Wavelet-like orthonormal bases for the lowest Landau level." Journal of Physics A: Mathematical and General 27, no. 7 (April 7, 1994): 2471–81. http://dx.doi.org/10.1088/0305-4470/27/7/024.

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48

Takano, S., and H. Kawamura. "On the Lowest Landau Level of Electrons in Bismuth." Progress of Theoretical Physics Supplement 57 (May 14, 2013): 199–203. http://dx.doi.org/10.1143/ptp.57.199.

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49

Hansson, T. H., J. M. Leinaas, and S. Viefers. "Field theory of anyons in the lowest Landau level." Nuclear Physics B 470, no. 3 (July 1996): 291–316. http://dx.doi.org/10.1016/0550-3213(96)00178-2.

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50

Klevtsov, Semyon. "Lowest Landau level on a cone and zeta determinants." Journal of Physics A: Mathematical and Theoretical 50, no. 23 (May 12, 2017): 234003. http://dx.doi.org/10.1088/1751-8121/aa6e0a.

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