Meissner Effect from Landau Problem

The Landau problem for inhomogeneous magnetic fields is examined in a very general context and several interesting analogies with the Nielsen–Olesen vortices are established. Firstly, we show that the Landau problem with non-homogeneous magnetic fields exhibits Meissner effect that is unstable unless two-body interactions are added and vortices emerge. Using the scaling freedom, we can write the Schrödinger equation in terms of the scales ratio κ = E/m ∝ 1 − T/Tc where the last identification is realized simply by using the Ginzburg–Landau theory. We find our equations are valid in the superconducting regime, and it is not possible for the Cooper pairs amplitude to reach to a constant, nonzero value, and therefore the theory is unstable. The supersymmetric quantum mechanics version, by completeness, is also considered.

Note:

5 pages, two columns, 1 figure. Comments welcomed

03.65.-w
71.70.Di
74.20.De
Superconductivity
quantum mechanics
supersymmetry
quantum mechanics: supersymmetry
Landau problem
Meissner effect
magnetic field

References(15)

Figures(1)

[1]

Superconductivity

J.R. Schrieffer
(
- Florida State U.
)
,
M. Tinkham
(
- Harvard U.
)

- Rev.Mod.Phys. 71 (1999) S313-S317
•
DOI:
- 10.1103/RevModPhys.71.S313

[2]

J. Klaers
,
J. Schmitt
,
F. Vewinger
,
M. Weitz

- Nature 468 (2010) 545

[3]

Bose-Einstein Condensation of Dark Matter Axions

P. Sikivie
(
- Florida U.
)
,
Q. Yang
(
- Florida U.
)

- Phys.Rev.Lett. 103 (2009) 111301
•
e-Print:
- 0901.1106
•
DOI:
- 10.1103/PhysRevLett.103.111301

[4]

Evolution of cosmological perturbations in Bose-Einstein condensate dark matter

T. Harko
(
- Hong Kong U.
)

- Mon.Not.Roy.Astron.Soc. 413 (2011) 3095-3104
•
e-Print:
- 1101.3655
•
DOI:
- 10.1111/j.1365-2966.2011.18386.x

[4]

Cosmological dynamics of dark matter Bose-Einstein Condensation

T. Harko
(
- Hong Kong U.
)

- Phys.Rev.D 83 (2011) 123515
•
e-Print:
- 1105.5189
•
DOI:
- 10.1103/PhysRevD.83.123515

[4]

Bose-Einstein-condensed scalar field dark matter and the gravitational wave background from inflation: new cosmological constraints and its detectability by LIGO

Bohua Li
(
- Texas U., Astron. Dept.
)
,
Paul R. Shapiro
(
- Texas U., Astron. Dept.
)
,
Tanja Rindler-Daller
(
- Michigan U., MCTP and
- Vienna U., Inst. Astron.
)

- Phys.Rev.D 96 (2017) 6, 063505
•
e-Print:
- 1611.07961
•
DOI:
- 10.1103/PhysRevD.96.063505

[5]

On Anyon Superconductivity

- Int.J.Mod.Phys.B 3 (1989) 1001,
•
DOI:
- 10.1142/S0217979289000725

[6]

An Introduction to the Ginzburg-Landau Theory of Phase Transitions and Nonequilibrium Patterns

P.C. Hohenberg
,
A.P. Krekhov

e-Print:
- 1410.7285

[7]

Vortex Line Models for Dual Strings

Holger Bech Nielsen
(
- Bohr Inst.
)
,
P. Olesen
(
- Bohr Inst.
)

- Nucl.Phys.B 61 (1973) 45-61,
•
DOI:
- 10.1016/0550-3213(73)90350-7

[8]

Gauge fields in condensed matter. Vol. 1: Superflow and vortex lines. Disorder fields, phase transitions

H. Kleinert

[9]

On the Magnetic properties of superconductors of the second group

A.A. Abrikosov
(
- Moscow, Inst. Phys. Problems
)

- Sov.Phys.JETP 5 (1957) 1174-1182,
- Zh.Eksp.Teor.Fiz. 32 (1957) 1442-1452

[10]

SUPERSYMMETRIC NONRELATIVISTIC QUANTUM MECHANICS

J. Gamboa
(
- Chile U., Santiago
)
,
J. Zanelli
(
- CECS, Valdivia
)

- Phys.Lett.B 165 (1985) 91-93,
- Phys. Lett. B165 ( 1985) 91-93
•
DOI:
- 10.1016/0370-2693(85)90697-5

[11]

Ground-state wave-function "representation"

E. Gozzi
(
- City Coll., N.Y.
)

- Phys.Lett.B 129 (1983) 432-436,
- Nucl.Phys.A 279 (1977) 532-532 (erratum),
- Phys.Lett.B 134 (1984) 477-477 (erratum)
•
DOI:
- 10.1016/0370-2693(83)90134-X

[12]

Dynamical Breaking of Supersymmetry

Edward Witten
(
- Princeton U.
)

- Nucl.Phys.B 188 (1981) 513,
- IN *FERRARA, S. (ED.): SUPERSYMMETRY, VOL. 1*, 443-484. (NUCL. PHYS. B188 (1981) 513-554) AND PREPRINT - WITTEN, E. (REC.JUL.81) 72 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0550-3213(81)90006-7

[13]

Supersymmetry and quantum mechanics

Fred Cooper
(
- Los Alamos
)
,
Avinash Khare
(
- Bhubaneswar, Inst. Phys.
)
,
Uday Sukhatme
(
- Illinois U., Chicago
)

- Phys.Rept. 251 (1995) 267-385
•
e-Print:
- hep-th/9405029
•
DOI:
- 10.1016/0370-1573(94)00080-M