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 Events
PhD Candidate: Cindy M Blois
Mathematics, UBC
Mon 29 Jun 2015, 12:30pm SPECIAL
One Time Event
Room 203, Graduate Student Centre, 6371 Crescent Rd., UBC
Doctoral Exam: Functional Integral Representations for Quantum Many-Particle Systems
Room 203, Graduate Student Centre, 6371 Crescent Rd., UBC
Mon 29 Jun 2015, 12:30pm-2:30pm

Details

ABSTRACT: Formal functional integrals are commonly used as theoretical tools and as sources of intuition for predicting phase transitions of many-particle systems in Condensed Matter Physics. In this thesis, we derive rigorous versions of these functional integrals for two types of quantum many-particle systems.

We start with a brief review of quantum statistical mechanics and the formalism of coherent states, which form the basis for our analysis. For a mixed gas of bosons and/or fermions interacting on a finite lattice with a general Hamiltonian that preserves the total number of particles in each species, we rigorously derive a functional integral representation for the partition function, using a large-field cutoff for the boson fields. We then expand the resulting “action” in powers of the fields and find a recursion relation for the coefficients. In the case of a 2-body interaction (such as the Coulomb interaction), we also find bounds on the coefficients, which give a domain of analyticity for the action. This domain is large enough for use of the action in the functional integral, provided that the large-field cutoffs are taken to grow not too quickly. Next, we study a system of electrons and phonons interacting in a finite lattice, using the Holstein Hamiltonian. We again rigorously derive a coherent-state functional integral representation for the partition function of this system and then prove that the action in the functional integral is an entire-analytic function of the fields. However, since the Holstein Hamiltonian does not preserve the total number of bosons, our approach for the previous system requires some modification. In particular, we repeatedly use Duhamel expansions in powers of the interaction, rather than sums over particle numbers.
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Jean-luc Doumont
Tue 30 Jun 2015, 10:00am
PIMS Seminars and PDF Colloquiums
TRIUMF auditorium (on the UBC campus)
Structuring your research paper
TRIUMF auditorium (on the UBC campus)
Tue 30 Jun 2015, 10:00am-12:00pm

Abstract


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University of Alberta
Tue 30 Jun 2015, 3:00pm
Algebraic Groups and Related Structures
MATH 126
Upper-homogeneous varieties
MATH 126
Tue 30 Jun 2015, 3:00pm-4:00pm

Abstract

We introduce a new class of algebraic varieties which is closed under products and embraces, e.g., projective homogeneous varieties, generically split varieties, and standard norm varieties (associated to symbols in Galois cohomology groups). We prove for this class the characterization of canonical p-dimension in terms of algebraic cycles previously known for projective homogeneous and generically split varieties. As an application, we extend to this class the incompressibility criterion of products previously known only for certain type of projective homogeneous varieties.
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George Bluman
UBC Math
Fri 3 Jul 2015, 2:30pm
Symmetries and Differential Equations Seminar
Math 125
Nonlocally related systems and nonlocal symmetries III
Math 125
Fri 3 Jul 2015, 2:30pm-3:30pm

Abstract

This lecture will be a continuation of the previous one with illustrative examples.
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