Report on Application of Superconductos Submitted by PANKAJ JINAGAL RRAHUL BIDIYASAR 2014IMSPH010 Submitted to Dr

Report
on
Application of Superconductos
Submitted by
PANKAJ JINAGAL
RRAHUL BIDIYASAR
2014IMSPH010
Submitted to
Dr. Ajit kumar Patra
Department of Physics
School of Physical Sciences
Central University of Rajasthan
Report
on Application of SuperconductosSubmitted by
PANKAJ JINAGAL
RRAHUL BIDIYASAR
2014IMSPH010
Submitted to
Dr. Ajit kumar Patra
Department of Physics
School of Physical Sciences
Central University of Rajasthan

Contents
TOC o “1-3” h z u 1 Introduction 5 HYPERLINK l “_Toc8223” h 2 Different types of models of interacting spins………………………………………… 5
2.1 Heisenberg ModelPAGEREF _Toc8223 h5
2.2 Majumdar Ghosh Chain5 2.3 Haldane Shastry Model63 Theorems7 3.1 Lieb – Mattis Theorem PAGEREF _Toc8227 h7 3.2 Marshall’s Sign Rule 7 3.3 Lieb, Schultz And Mattis (LSM) TheoremPAGEREF _Toc8229 h8 3.4 Oshikawa, Yamanaka, And AffleckTheorem…………………………………………..8
3.5 Mermin – Wagner’s Theorem………………………………………………………………..9
4 Results………………………………………………………………………………………………………9
4.1 The Bathe Ansatz (BA)…………………………………………………………………………..9
4.2 The Majumdar Ghosh Chain………………………………………………………………..11
4.3 The Affleck – Kennedy – Lieb – Tasaki (AKLT) Model…………………………….13
5. Conclusions…………………………………………………………………………………………….14
6. References……………………………………………………………………………………………..15

Abstract
Superconductivity is one of the most dynamic field of research in solid state physics. This report includes studying of various practical and real life applications of superconductors, it also emphasis on need of superconductors in modern prospective. We start with general idea about superconductors and various phenomenon governing superconductivity.

INTRODUCTION
We all know that electrical resistivity is a function of temperature such that it decreases with decreases in temperature. As we decrease the temperature the thermal vibrations of atoms decreases and the conduction electrons are very less scattered by surrounding atoms, this is the basic idea behind the superconductivity.

What is Superconductivity?
The phenomenon of complete loss of resistivity by certain metals and alloys when they are cooled below a certain temperature is called the superconductivity. The temperature at which a normal conductor changes to a zero magnetic field is called the critical temperature ( Tc ).

e.g. Be, Bi and Fe show superconductivity.

Let us take an example of mercury which converts into superconductor at 4.2 K

1.2 Cause of superconductivity-
The cause of superconductivity is explained by BCS theory. According to this theory, two electrons in a free space are repelled by each other but in condensed form the is modified due to interaction of electrons with crystal lattice. In specific substances this interaction becomes attractive and binds electrons together and becomes attractive and binds electrons and are known as Cooper pairs.

In superconductors the electrons are not free such that they are in the form of cooper pairs which drift through the material on the application of electric field. At very low temperature phonons do not have enough energy to break the cooper pairs and these pairs swiftly pass through the lattice without experiencing any resistance.

1.3 Principal properties of superconductors
The superconductors have property to retain current for a very long time.

Superconductors generally found in metals with valence electrons lie between 2 to 8
The magnetic field will not able to pass through the superconductors, this phenomenon is known as the Missner Effect.

When the value of current passing through the superconductor is increased far off a specific value then the superconductor becomes a normal conductor.

Superconductivity occurs in materials having high normal resistivities.

Good conductors at room temperature are not superconductors, and superconducting materials are not very good conductors at room temperature as the normal metals.

2.Practical Applications of superconductors
Superconductors have widespread uses in almost every field. They are used in making of several devices .There are many uses of superconductors each with different application such as Magnetic Resonance Imaging (MRI), high speed trains (Maglev) and the list is never ending so here we will discuss some of the important applications of superconductors.

Magnetic Resonance Imaging (MRI)
Magnetic Resonance Imaging is a technique for diagnosis and imaging of various body organs .The most important component of MRI is the magnet. When a patient enters through a horizontal tube ,this is whole a magnet ranging from front to back but this is not a normal magnet we require magnet with extremely high magnetic field which can be produced with the help of superconductors. All MRI uses superconducting magnet which have many coils of wire through which electricity is passed and creating a very high magnetic field of the order of tesla.

Superconducting transmission lines
We all know that a large part of electricity is wasted during transmission because of Joule heating. This is mainly due to the resistance offered by metal wires and as we know that superconductors offers almost negligible resistance therefore they can be used in transmission lines. Superconductors used in these are usually niobium-titanium and for cooling purpose liquid helium is used .But superconducting cables in real have sources of loss which is be taken into consideration such as no cooling is perfect so there are some losses due imperfect cooling. Similar to metal transmission lines superconducting cables also have dielectric losses and in practice the superconducting transmission is very expensive and only feasible in high load areas such as large cities as they require large amount of electricity. Superconducting lines are difficult to implement due to its high costing.

High speed trains (Maglev)
Maglev are high speed trains which can acquire speed up to 400-600km/h. In Maglev superconducting magnets are used, superconducting magnets are basically electromagnets that are cooled to very low temperature due to which power of magnetic field increases to many times. The working of the train based on the fact that it is placed over the guideway and magnets on top of the guideway are designed to repel similar poles of magnet in the bottom of maglev. This pushes the maglev upward in hovering position. The force required to levitate the Maglev is provided by strong magnetic field, we can use normal magnets for this process but power is low and limited so to produce more power superconducting coils are used, the coils are conventional superconductors so require very low temperature so always surrounded by liquid helium.

5. CONCLUSION
In sections 1 – 4, a brief overview of low- dimensional quantum magnets has been given. The study on quantum magnetism has witnessed an unpredicted growth in research activity in the last decade. Powerful theorems have been proposed and the exact results are obtained.
6. REFRENCES
1 B. Indrani, Quantum magnets: a brief overview (2008)
2 C. K. Majumdar and D.K. Ghosh, J. Math. Phys. 10, 1388
3 E. H. Lieb and D.C. Mattis, J. Math. Phys. 3, 749
4 Auerbach, Assa, Interacting Electrons and Quantum Magnetism
5 http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html6 https://en.wikipedia.org/wiki/Category:Quantum_magnetism7 LaTeX (to generate this report)