BOSE-EINSTEIN CONDENSATION AND LIQUID

HELIUMSTATISTICAL

THERMODYNAMICSRAJARSHI GUHA(07302009)ANKIT SHARMA(07302011)

M.TECH. 1st YEAR

APPLICATIONS OF BOSE-EINSTEIN CONDENSATION

• Bose-Einstein condensation is mostly used in chemical physics and quantum statistics.

• This provides the theory of how condensation of Bosons occurs at very low temperatures

• Anomalous behavior of liquid helium and super-fluidity can be described by this phenomena

• An important application of liquid helium has been in the study of superconductivity and for the applications of superconducting magnets

• This phenomena is a leading research field in modern physics and chemistry

WHAT IS BOSE-EINSTEIN CONDENSATION

• In 1924, a paper by Satyendra Nath Bose and Albert Einstein described Bose-Einstein statistics and introduced a particle concept called “Bosons”.

• At very low temperatures the collection of bosons into a single state, i.e. into their ground states is called Bose-Einstein condensation

Bose-Einstein condensation

                                                                                          

Nobel condensate - how alkali metal atoms come together as the temperature is decreased. The image shows Bose-Einstein condensation at, from left to right, 400, 200, and 50 nK.

BOSE-EINSTEIN STATISTICS AND BOSONS

• The Bose-Einstein distribution describes the statistical behavior of particles carrying an integer value of intrinsic angular momentum (spins), called Bosons.

• At low temperatures, bosons can behave very differently than Fermions because an unlimited number of them can collect into the same energy state, this phenomenon called "condensation“.

LIQUID HELIUM AND ITS ANOMALOUS BEHAVIOR

• When a liquid becomes superfluid its atoms suddenly lose all their randomness and move in a coordinated manner in each movement. This causes the liquid to lack all inner friction

• How IPP(Infinite Particle Physics) Explains Superfluidity of Helium 4 :

Perhaps, when helium atoms lose most of their thermal motions, they acquire the ability to form linear polymer sheets of tremendous tenacity whose affinity for adjacent polymer sheets is essentially nil. One might say that the property crucial to superfluidity is the complete lack of bonding between these polymer sheets and any materials they come in contact with.

• When helium is cooled to a critical temperature of 2.17 K (called its lambda point), a remarkable discontinuity in heat capacity occurs

• The liquid density drops, and a fraction of the liquid becomes a zero viscosity "super-fluid".

• Super-fluidity arises from the fraction of helium atoms which has condensed to the lowest possible energy.

The He-4 heat capacity curve looks like greek word lambda and thus it is lambda transition

THE CRITICAL TEMPERATURE

• This transition occurs below a critical temperature, which for a uniform three-dimensional gas consisting of non-interacting particles with no apparent internal degrees of freedom is given by:

Tc = 0.0837h^2/(mKB) (N/V)^2/3

Where h is plank constant, m is mass per boson, KB is Boltzmann constant and N is the total number of particles.

Let n0 denotes mean occupation no. in 0th energy state, then

n0/N = 1-(T/Tc)^ 3/2 for T< Tc describes the condensation.

  

Specific Heat V/s Temperature Curve of Helium

ELUCIDATION OF LIQUID He-4 BEHAVIOR BY BEC

• BEC is a first order process, but the system has a uniform density rather than two different densities during transition because condensation occurs in momentum space rather than co-ordinate space and condensed phase has zero momentum

• The heat capacity curves for liquid He-4 and ideal BE gas is very similar

• BEC describes the transition except the fact that lambda transition is not 1st order as heat capacity diverges near Tc

• One can’t accept complete agreement because liquid He-4 is an inextricable combination of quantum statistics and intermolecular interactions.

• BEC can’t predict liquid He-3 behavior as it obeys Fermi-Dirac statistics

WORKS THAT FOLLOW BEC

• After appearance of BEC it is applied by various scientists to describe different phenomena, some of these are_

• 1. explanation of thermal radiation by Plank,• 2.proposal of London that liquid helium can be considered as a degenerate

BE gas, with this formula n/n0 = 1- (T/T0)^s T<T0, T0 is degeneracy temperature, s=1.5 for BE gas, 3. superfluidity explanation by Landau,

• 4. Onsager-Penrose derivation that roughly 8% of atoms are “condensed” in liquid helium,

• 5. BCS theory of superconductivity,

• 6. reaching near 0K by laser cooling and magnetic traps etc.

Liquid Helium Superfluidity

RECENT RESEARCH WORKS AND PROBLEMS

• The conditions for achieving a Bose-Einstein condensate are quite extreme. • The participating particles must be considered to be identical, and this is a

condition that is difficult to achieve for whole atoms.

• The condition of indistinguishability requires that the deBroglie wavelengths of the particles overlap significantly.

• This requires extremely low temperatures so that the deBroglie wavelengths will be long, but also requires a fairly high particle density to narrow the gap between the particles.

• The use of laser cooling and the trapping of ultra-cold atoms with magnetic traps has produced temperatures in the nanokelvin range.

• Cornell and Wieman along with Ketterle of MIT received the 2001 Nobel Prize in Physics "for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates".

CONCLUSIONS

BEC and liquid helium are very interrelated and there are many physical phenomenon associated with it.

This field is one of the frontiers in modern physics and still producing Noble laureates.

From mere theory and derivation, BE statistics then applied to liquid helium and even after its 90 years of existence new applications keep coming.