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Statistical mechanics of nonrelativistic charged particles in a constant magnetic field.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1999 · Unclear · Insufficient evidence

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A theoretical treatment (effective action method) of nonrelativistic charged particles in a constant magnetic field is presented for arbitrary spatial dimension D (assuming D≥3). For D≥5 a phase transition with a Bose condensate is reported, and the condensat…

Study snapshot

PublicationPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1999
Study typeother
Reported directionUnclear
Evidence ratingInsufficient

Abstract

The statistical mechanics of a system of nonrelativistic charged particles in a constant magnetic field is discussed. The spatial dimension D is arbitrary, with D>or=3 assumed. Calculations are presented from first principles using the effective action method. For D>or=5 the system has a phase transition with a Bose condensate. We show how the effective action method deals in a very natural way with the condensate, and study its role in the magnetization of the gas. For large values of the magnetic field we show how the magnetized gas in D spatial dimensions behaves like the free Bose gas in D-2 spatial dimensions. Even though for D=3 the magnetized gas does not have a phase transition for any nonzero value of the magnetic field, we show how the specific heat starts to resemble the result for the free gas as the magnetic field is reduced. A number of analytical approximations for the magnetization and specific heat are given, and compared with numerical results. In this way we are able to study in precise detail how the B-->0 limit of the magnetized gas is achieved.

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AI evidence extraction

Structured fields below were generated from the paper’s abstract and metadata to make the evidence easier to inspect. Automated extraction may be incomplete or incorrect; verify important details against the original paper.

Study typeother
Effect directionunclear
PopulationNot supplied
Sample sizeNot supplied
ExposureNot supplied
Evidence strengthInsufficientConfidence: 74% · Peer reviewed: yes

Main findings

A theoretical treatment (effective action method) of nonrelativistic charged particles in a constant magnetic field is presented for arbitrary spatial dimension D (assuming D≥3). For D≥5 a phase transition with a Bose condensate is reported, and the condensate’s role in magnetization is analyzed; for large magnetic fields the system in D dimensions behaves like a free Bose gas in D−2 dimensions. For D=3 no phase transition occurs for any nonzero magnetic field, but the specific heat approaches the free-gas result as the field is reduced, with analytical approximations compared to numerical results.

Outcomes measured

  • phase transition / Bose condensate (theoretical)
  • magnetization (theoretical)
  • specific heat (theoretical)
  • B→0 limit behavior (theoretical)

Limitations

  • The work is theoretical/statistical-mechanics modeling rather than an empirical exposure/health study.
  • No biological or epidemiological outcomes are assessed in the abstract.
  • No exposure metrics (frequency, SAR, field strength values) are provided beyond a constant magnetic field B.
View raw extracted JSON
{
  "study_type": "other",
  "exposure": {
    "band": null,
    "source": null,
    "frequency_mhz": null,
    "sar_wkg": null,
    "duration": null
  },
  "population": null,
  "sample_size": null,
  "outcomes": [
    "phase transition / Bose condensate (theoretical)",
    "magnetization (theoretical)",
    "specific heat (theoretical)",
    "B→0 limit behavior (theoretical)"
  ],
  "main_findings": "A theoretical treatment (effective action method) of nonrelativistic charged particles in a constant magnetic field is presented for arbitrary spatial dimension D (assuming D≥3). For D≥5 a phase transition with a Bose condensate is reported, and the condensate’s role in magnetization is analyzed; for large magnetic fields the system in D dimensions behaves like a free Bose gas in D−2 dimensions. For D=3 no phase transition occurs for any nonzero magnetic field, but the specific heat approaches the free-gas result as the field is reduced, with analytical approximations compared to numerical results.",
  "effect_direction": "unclear",
  "limitations": [
    "The work is theoretical/statistical-mechanics modeling rather than an empirical exposure/health study.",
    "No biological or epidemiological outcomes are assessed in the abstract.",
    "No exposure metrics (frequency, SAR, field strength values) are provided beyond a constant magnetic field B."
  ],
  "evidence_strength": "insufficient",
  "confidence": 0.74,
  "peer_reviewed_likely": "yes",
  "keywords": [
    "constant magnetic field",
    "nonrelativistic charged particles",
    "effective action method",
    "Bose condensate",
    "phase transition",
    "magnetization",
    "specific heat",
    "dimensional reduction"
  ],
  "suggested_hubs": []
}
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AI-extracted fields are generated from the abstract and metadata and may be incomplete or incorrect. This material is for informational purposes and is not medical advice.

Identifiers and source

DOI: 10.1103/physreve.60.5275
PubMed: 11970396

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