- Text
- Superconductivity,
- Oscillations,
- Publishing,
- Superfluidity,
- Magnetic,
- Superconductors,
- Electron,
- Superconducting,
- Electrons,
- Density,
- ÑÐ¸Ð·Ð¸ÐºÐ¾ÑÐµÑ Ð½Ð¸Ðº.ÑÑ

Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and Superfluidity where a and b are model parameters. Using the principle of minimum free energy of the system in a steady state, we can find the relation between these parameters: d(∆W ) dn s = −a + b · n s = 0. (4.13) Whence b = a n s (4.14) and the energy gain in the transition to an ordered state: ∆W = − a 2 n s. (4.15) The reverse transition from the superconducting state to a normal state occurs at the critical magnetic field strength, H c . This is required to create the density of the magnetic energy H2 c 8π . According to the above description, this equation is therefore obtained: H 2 c 8π = a 2 n s. (4.16) In order to express the parameter a of GL-theory in terms of physical characteristics of a sample, the density of “superconducting” carriers generally charge from the London’s equation (4.8). 2 The important step in the Ginzburg-Landau theory is the changeover of the concentration of superconducting carriers, n s , to the order parameter Ψ |Ψ(x)| 2 = n s . (4.17) At this the standard Schrodinger equation (in case of one dimension) takes the form: − 2m [∇Ψ(x)]2 − aΨ 2 (x) + b 2 Ψ4 (x) = E. (4.18) Again using the condition of minimum energy dE dΨ = 0 (4.19) 2 It should be noted that due to the fact that the London equation does not correctly describes the ratio of the penetration depth with a density of carriers, one should used the revised equation (9.13) in order to find the a. 34 Science Publishing Group

Chapter 4 Basic Milestones in the Study of Superconductivity after the simple transformations one can obtain the equation that is satisfied by the order parameter of the equilibrium system: aΨ + bΨ|Ψ| 2 + 1 4m e ( i∇ + 2e c A ) 2 Ψ = 0. (4.20) This equation is called the first Ginzburg-Landau equation. It is nonlinear. Although there is no analytical solution for it, by using the series expansion of parameters, we can find solutions to many of the problems which are associated with changing the order parameter. Such there are consideration of the physics of thin superconducting films, boundaries of superconductor-metal, phenomena near the critical temperature and so on. The variation of the Schrodinger equation (4.18) with respect the vector potential A gives the second equation of the GL-theory: j s = ie 2m e (Ψ ∗ ∇Ψ − Ψ∇Ψ ∗ ) − 2e2 m e c |Ψ|2 A. (4.21) This determines the density of superconducting current. This equation allows us to obtain a clear picture of the important effect of superconductivity: the magnetic flux quantization. 4.3 Experimental Data That Are Important for Creation of the Theory of Superconductivity 4.3.1 Features of the Phase Transition Phase transitions can occur with a jump of the first derivatives of thermodynamic potential and with a jump of second derivatives at the continuous change of the first derivatives. In the terminology of Landau, there are two types of phase transitions: the 1st and the 2nd types. Phenomena with rearrangement of the crystal structure of matter are considered to be a phase transition of the 1st type, while the order-disorder transitions relate to the 2nd type. Measurements show that at the superconducting transition there are no changes in the crystal structure or the latent heat release and similar phenomena characteristic of first-order transitions. On the contrary, the specific Science Publishing Group 35

- Page 3 and 4: Superconductivity and Superfluidity
- Page 5 and 6: Annotation 1. The prevailing now BC
- Page 7: Annotation depends on the ratio uni
- Page 10 and 11: Contents II The Development of the
- Page 12 and 13: Contents 9.2 The Magnetic Energy an
- Page 15 and 16: Chapter 1 Is It Possible for a Phys
- Page 17 and 18: Chapter 1 Is It Possible for a Phys
- Page 19 and 20: Chapter 1 Is It Possible for a Phys
- Page 21 and 22: Chapter 1 Is It Possible for a Phys
- Page 23 and 24: Chapter 2 About Pseudo-Theories of
- Page 25 and 26: Chapter 2 About Pseudo-Theories of
- Page 27 and 28: Chapter 2 About Pseudo-Theories of
- Page 29 and 30: Chapter 2 About Pseudo-Theories of
- Page 31 and 32: Chapter 2 About Pseudo-Theories of
- Page 33: Part II The Development of the Scie
- Page 36 and 37: Superconductivity and Superfluidity
- Page 38 and 39: Superconductivity and Superfluidity
- Page 40 and 41: Superconductivity and Superfluidity
- Page 42 and 43: Superconductivity and Superfluidity
- Page 44 and 45: Superconductivity and Superfluidity
- Page 48 and 49: Superconductivity and Superfluidity
- Page 50 and 51: Superconductivity and Superfluidity
- Page 52 and 53: Superconductivity and Superfluidity
- Page 54 and 55: Superconductivity and Superfluidity
- Page 56 and 57: Superconductivity and Superfluidity
- Page 58 and 59: Superconductivity and Superfluidity
- Page 60 and 61: Superconductivity and Superfluidity
- Page 62 and 63: Superconductivity and Superfluidity
- Page 65 and 66: Chapter 5 Superfluidity The first s
- Page 67 and 68: Chapter 5 Superfluidity It happened
- Page 69 and 70: Chapter 5 Superfluidity worked on a
- Page 71: Part III Superconductivity, Superfl
- Page 75 and 76: Chapter 6 Superconductivity as a Co
- Page 77 and 78: Chapter 6 Superconductivity as a Co
- Page 79 and 80: Chapter 6 Superconductivity as a Co
- Page 81 and 82: Chapter 6 Superconductivity as a Co
- Page 83 and 84: Chapter 6 Superconductivity as a Co
- Page 85: Chapter 6 Superconductivity as a Co
- Page 88 and 89: Superconductivity and Superfluidity
- Page 90 and 91: Superconductivity and Superfluidity
- Page 92 and 93: Superconductivity and Superfluidity
- Page 94 and 95: Superconductivity and Superfluidity
- Page 96 and 97:
Superconductivity and Superfluidity

- Page 98 and 99:
Superconductivity and Superfluidity

- Page 100 and 101:
Superconductivity and Superfluidity

- Page 102 and 103:
Superconductivity and Superfluidity

- Page 104 and 105:
Superconductivity and Superfluidity

- Page 106 and 107:
Superconductivity and Superfluidity

- Page 108 and 109:
Superconductivity and Superfluidity

- Page 110 and 111:
Superconductivity and Superfluidity

- Page 112 and 113:
Superconductivity and Superfluidity

- Page 114 and 115:
Superconductivity and Superfluidity

- Page 116 and 117:
Superconductivity and Superfluidity

- Page 118 and 119:
Superconductivity and Superfluidity

- Page 120 and 121:
Superconductivity and Superfluidity

- Page 122 and 123:
Superconductivity and Superfluidity

- Page 124 and 125:
Superconductivity and Superfluidity

- Page 126 and 127:
Superconductivity and Superfluidity

- Page 128 and 129:
Superconductivity and Superfluidity

- Page 131:
Part IV Conclusion

- Page 134 and 135:
Superconductivity and Superfluidity

- Page 137 and 138:
References [1] W. Gilbert: De magne

- Page 139 and 140:
References [33] Bethe H., Sommerfel