Online TA Profiles
Saibal Mitra, PhD (IP)
OTA ID#: 104454

Education Experience: MSc, Theoretical Physics, University of Utrecht, 1999
PhD (IP), Theoretical Physics, University of Amstedam, 2004
Focus of Study: Research on: Exactly solvable models, percolation, loop models, exact parity model.
Publications: Refereed journal articles on dark matter:

S. Mitra, ''Detecting dark matter in electromagnetic field penetration experiments'', Phys. Rev. D 74, 043532 (2006)
[http://arxiv.org/abs/astro-ph/0605369].

S. Mitra, ''Has DAMA Detected Self-Interacting Dark Matter?'', Phys. Rev. D 71, 121302 (2005) [http://arxiv.org/abs/astro-ph/0409121].

S. Mitra, ''Uranus's anomalously low excess heat constrains strongly interacting dark matter'', Phys. Rev. D 70, 103517 (2004) [http://arxiv.org/abs/astro-ph/0408341].

R. Foot and S. Mitra, ''Detecting mirror matter on Earth via its thermal imprint on ordinary matter'', Phys. Lett. A 315, 178-183 (2003) [http://arxiv.org/abs/cond-mat/0306561].

R. Foot and S. Mitra, ''Have mirror micrometeorites been detected?'', Phys. Rev. D 68, 071901 (2003) [http://arxiv.org/abs/hep-ph/0306228].

S. Mitra and R. Foot, ''Detecting dark matter using centrifuging techniques'', Phys. Lett. B 558, 9-14 (2003) [http://arxiv.org/abs/astro-ph/0301229].

R. Foot and S. Mitra, ''Mirror matter in the solar system: New evidence for mirror matter from Eros'', Astropart. Phys. 19, 739-753 (2003) [http://arxiv.org/abs/astro-ph/0211067].

R. Foot and S. Mitra, ''Ordinary atom-mirror atom bound states: A new window on the mirror world'', Phys. Rev. D 66, 061301 (2002) [http://arxiv.org/abs/hep-ph/0204256].

Refereed journal articles on mathematical physics:

S. Mitra, ''Exact asymptotics of the characteristic polynomial of the symmetric Pascal matrix'', Journal of Combinatorial Theory A 116, 30-43 (2009) [http://arxiv.org/abs/0708.1763].

S. Mitra and B. Nienhuis, ''Exact conjectured expressions for correlations in the dense O(1) loop model on cylinders'', J. Stat. Mech.: Theor. Exp. (2004) P10006 [http://arxiv.org/abs/cond-mat/0407578].

S. Mitra and B. Nienhuis, J. de Gier and M. T. Batchelor, ''Exact expressions for correlations in the ground state of the dense O(1) loop model'', J. Stat. Mech.: Theor. Exp. (2004) P09010 [http://arxiv.org/abs/cond-mat/0401245].

S. Mitra, ''Expansions about Free-Fermion Models'', J. Math. Phys. 45 (2004) 100-106 [http://arxiv.org/abs/math-ph/0303023].

S. Mitra and B. Nienhuis, ''Osculating Random Walks on Cylinders'', Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, (2003), pp. 259-264 [http://arxiv.org/abs/math-ph/0312036].

J. de Gier, M.T. Batchelor, B. Nienhuis and S. Mitra, ''The XXZ spin chain at $Delta=- {1/2}$: Bethe roots, symmetric functions and determinants'', J. Math. Phys. 43, (2002) 4135-4146 [http://arxiv.org/abs/math-ph/0110011].
Work Experience: December 1999 - Present

Research Assistant at:
Institute for Theoretical Physics,
University of Amsterdam.

Teaching: Problem sessions for introductory course in statistical physics
Outside Interests: Star gazing, various sports and computers.
Message to Students
and/or Parents:		 The only way to learn mathematics or physics is by solving difficult problems yourself. In case of difficulties, a teacher can help you by showing where you went wrong or what you don't understand yet.


After receiving help, you should always try to solve a similar problem by yourself.
Postings Answered: 298
Cumulative OTA Rating: 4.9/5  What is OTA Rating?
Top Solutions Downloads
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  1. Derive the formula for the multiplicity (entropy) of the two state paramagnet in the lagre N limit and when the number of excess spins relative to N is small. - For a single large two-state paramagnet, the multiplicity function is very sharply peaked about N/2. (a) Use Stirling's approximation to estimate the height of the peak in the multiplicity fun ...
  2. Expansion coefficient and the Lennard-Jones potential. - Consider a classical particle moving in a one-dimensional potential well u(x). The particle is in thermal equilibrium with a reservoir at temperature T, so the probabilities of its various states are ...
  3. Waiting line problem - Speedy oil provides a single channel automobile oil change and lubrication service. Customers provide an arrive rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals fol ...
  4. Linear Programming - Solve the following linear programming problem using the graphical solution procedure: Maximize 5A +5B The constraints are: 1A <= 100 1 B <= 80 2A+4B <= 400 A,B >=0
  5. Entropy and chemical potential - For a diatomic gas near room temperature, the internal partition function is simply the rotational partition function multiplied by the degeneracy Ze of the electronic ground state. (a) Show that ...
  6. Find the probability that they meet again after N steps. - This is from Reif's Statistical and Thermal Physics: Two drunks start out together at the origin, each having equal probability of making a step to the left or right along the x-axis. Find the proba ...
  7. An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of 4.5x107m/s at an angle of 60°. Determine the wavelength of the X-ray source. - An X-ray source of unknown wavelength is directed at a carbon sample. An electron is scattered with a speed of 4.5x107m/s at an angle of 60°. Determine the wavelength of the X-ray source.
  8. Order-of-magnitude calculations. - Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thou ...
  9. Calculate the speed of two meteoroids at their closest point relative to Earth from a given initial speed at some given distance from Earth. - Two meteoroids are heading for earth. Their speeds as they cross the moon's orbit are 2.0 km/s. The second misses the earth by 5000 km. What is its speed at its closest point?
  10. Potential energy and chemical potential. - See attached file.
  11. Derive the Sackur-Tetrode equation using the microcanonical ensemble - Derive the formula for the entropy of an ideal monoatomic gas using the microcanonical ensemble. This formula is known as the Sackur-Tetrode equation.
  12. Molecules escaping Earth's gravity. - Escape velocity near Earth's surface is 11 km/s which means that a particle near Earth's surface traveling faster than about 11 km/s will have enough kinetic energy to completely escape from Earth's g ...
  13. Derive hooke's law and find the "elastic entropy". - Polymers, like rubber, are made of very long molecules that tangle into a configuration that has lots of S. A crude model of a rubber band contains N links, all of equal length L, which can only poin ...
  14. Semi-infinite square well. - Consider the semi-infinite square well given by V(x)=-Vo<0 for 0<=x<=a and V(x)=0 for x>a. There is an infinite barrier at x=0. A particle with mass m is in a bound state in this potential energy E<=0 ...
  15. Chemical potential for monatomic ideal gas. - Show that the equation: μ (T, P) = μ° (T) + kT ln (P/P°) is in agreement with the explicit formula for the chemical potential for a monatomic ideal gas. Show how to calculate μ° f ...
  16. A juggler is juggling a uniform rod one end of which is coated in tar and burning. He is holding the rod by the opposite end and throws it up so that, at the moment of release, it is horizontal, its Center of Mass is traveling vertically up at speed vo and it is rotating with angular velocity wo. To catch it, he wants to arrange that when it returns to his hand it will have made an integer number of complete rotations. What should vo be, if the rod is the have made exactly n rotations when it returns to his hand? - A juggler is juggling a uniform rod one end of which is coated in tar and burning. He is holding the rod by the opposite end and throws it up so that, at the moment of release, it is horizontal, its C ...
  17. Ehrenfest's theorem - Consider a 1-D free particle, describable as a wave packet at initial time t0. a) Show, applying Ehrenfest's theorem, that is a linear function of time and

    is a constant. b) Write the eq ...

  18. Find the entropy change of an ideal gas and of a van der Waals gas in case of isothermal expansion in which the volume increases by a factor alpha. Also, find the entropy change in case of a free expansion in which the volume increases by a factor alpha. In case of the free expansion of the van der Waals gas, find the temperature change. - Find the entropy change of an ideal gas and of a van der Waals gas in case of isothermal expansion in which the volume increases by a factor alpha. Also, find the entropy change in case of a free expa ...
  19. Einstein solids: macrostates and microstates - Consider a system of two Einstein solids, A and B, each containing 10 oscillators, sharing a total of 20 units of energy. Assume that the solids are weakly coupled, and that the total energy is fixed. ...
  20. A circus acrobat of mass M leaps straight up with initial velocity v(initial) from a trampoline. As he rises up, he takes a trained monkey of mass m off a perch at a height "h" above the trampoline. What is the maximum height attained by the pair? - A circus acrobat of mass M leaps straight up with initial velocity v(initial) from a trampoline. As he rises up, he takes a trained monkey of mass m off a perch at a height "h" above the trampoline. W ...
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