Physics  
Master of Science in Physics Master of Science in Materials Physics (ISP) Doctor of Philosophy in Physics  
Field(s) of Specialization (MSc, PhD)  
Experimental Condensed Matter Physics and Materials Science
Theoretical Physics
Biophysics
Dean
S. Ejaz Ahmed
Faculty of Mathematics and Science
Associate Dean
Cheryl McCormick
Faculty of Mathematics and Science
Core Faculty
Professors
Stephen Anco (Mathematics), Shyamal K. Bose (Physics), Douglas H. Bruce (Biological Sciences), David A. Crandles (Physics), Bozidar Mitrovic (Physics), Fereidoon S. Razavi (Physics), Maureen Reedyk (Physics), Kirill Samokhin (Physics), Art van der Est (Chemistry), Thomas Wolf (Mathematics)
Associate Professors
Thad A. Harroun (Physics), Alexander Odesskii (Mathematics), Edward Sternin (Physics)
Assistant Professor
Santo D'Agostino
Adjunct Professors
Ady Abdellatif, Richard Akis, Josef Dubicki, John Katsaras (NRC, Chalk River), Reinhard Kremer (MaxPlanck Institute, Germany), Ole Steuernagel (University of Hertfordshire, UK), Ranjini Tolakanahalli
Professors Emeritus
John E. Black (Physics), Stuart M. Rothstein (Chemistry), Ramesh C. Shukla (Physics)
Graduate Program Director
Maureen Reedyk
mreedyk@brocku.ca
Administrative Assistant
Elizabeth Horvath
9056885550, extension 3412
Mackenzie Chown B210
physics@brocku.ca
Graduate Studies Administrative Assistant
Beulah Alexander
9056885550, extension 3115
Mackenzie Chown D473
balexander@brocku.ca
International Coordinator, Graduate Programs
TBA
Senior Laboratory Coordinator/Demonstrator
Ivana Komljenovic Metcalf
Laboratory Demonstrator
Fulvio (Phil) Boseglav


Program Description  
The Department of Physics offers thesisbased MSc and PhD programs which focus on condensed matter physics, materials science, theoretical physics, and biophysics. Potential fields of research which may be pursued are described below. Students will gain extensive experience in research, critical thinking and essential communication and technical skills, which will prepare them for successful careers in industry, academic and other institutions and organizations. Handson use of our sophisticated equipment provides excellent job training and gives our graduates a significant advantage in the job market over those students who have only an undergraduate degree. The department also offers a 17month coursebased Master of Science in Materials Physics (MSMP) International Student Program (ISP) that provides intensive, handson graduate training in advanced experimental, theoretical, and computational techniques of modern materials science. The program aims to prepare highly knowledgeable and skilled graduates, who will be trained as materials physicists who can work as independent workers or in collaboration with others to fill jobs in industry, government agencies, research institutes and universities worldwide. The MSMP program focuses on skills to identify important and critical problems and to use appropriate methods and techniques to address them. Students will also learn how to communicate their results to a scientific audience as well as to nontechnical management staff, and to evaluate business and societal impact of their work without prejudice. These goals will be achieved through presentations at graduate research seminars and through the production of detailed technical laboratory and term reports conforming to the rigorous standards of scientific and technical publications in the fields of materials science and technology.  
Admission Requirements  
MSc Successful completion of four year Bachelor's degree, or equivalent, in Physics with a minimum B average. Applicants holding a degree without sufficient concentration in the area of the intended Master's degree, may be required to complete additional courses beyond those outlined as required for degree completion. The Graduate Record Examination (GRE) is recommended for international students, but not required. Agreement from a faculty advisor to supervise the student is also required for admission to the program. The Graduate Admissions Committee will review all applications and recommend admission for a limited number of suitable candidates. Parttime candidates may be considered. MSc in Materials Physics (ISP) Successful completion of a four year Bachelor's degree, or equivalent, from an accredited University, in Physics or a closely related discipline, with a minimum B average over the last two years of fulltime undergraduate study. Proof of English language proficiency will be required from all applicants. The minimum required score for entry is 80 on the TOEFL iBT (no section under 19), 6.5 on the IELTS (no section under 5.5). For a full listing of accepted tests, see https://brocku.ca/nextstep/internationalstudents/englishlanguageproficiency/. The Graduate Record Examination (GRE) is recommended for international students but not required. The Program Committee will review all applications and recommend admission for a limited number of suitable candidates. Applicants holding a degree without sufficient background in Physics may be required to complete additional qualifying undergraduate courses prior to an admission decision. PhD Students can be admitted into the PhD program through one of the following three options: (1) after successful completion of an MSc degree or equivalent in Physics or closely related discipline, with at least an 80% overall average; or (2) after one year in the Brock Physics MSc program. Students wishing to transfer to PhD Studies will be expected to have completed all master's coursework, with the exception of PHYS 5P91, with at least an 80% average. In addition, the student must submit a report on the progress made on the MSc thesis research, including a literature review and a PhD proposal, prior to the transfer. The transfer requires approval by the supervisory committee. (3) In exceptional cases, a student may be admitted directly to the PhD program with a fouryears honours Bachelor's degree, or the equivalent; his or her academic standing (normally, with at least an 80% major average) and research potential must be demonstrably commensurate with readiness for doctoral study. The Graduate Record Examination (GRE) is recommended for international students, but not required. Agreement from a faculty adviser to supervise the student is also required for admission to the program. The Graduate Admissions Committee will review all applications and recommend admission for a limited number of suitable candidates. Only fulltime PhD students will be admitted.  
Degree Requirements  
MSc All students must complete a research project that culminates in writing and defending a thesis. The program must include PHYS 5F90, PHYS 5P91 and four additional PHYS halfcredits. These must be at the 5(alpha)00 level or above with the exception of one halfcredit which may be at the 4(alpha)00 level. Additional credits may be required where a candidate is deficient in a particular area of study as determined by the supervisory committee. MSc students must enroll in the thesis course PHYS 5F90 each term. For fulltime students, the program is normally a six term or two year program. MSc in Materials Physics (ISP) Students accepted into the program are required to complete a fourweek Graduate Science Preparation Program (GSPP). The primary focus of GSPP is to prepare international students, whose first language is not English, for the academic demands of graduate programs at Brock University. This intensive English Program has been designed specifically for MSMP and other graduate students in the Sciences, and focuses on effective communication skills in English, community and cohort activities, and on the development of English skills in professional contexts. In exceptional cases, students may be exempted from GSPP. Over four subsequent terms of study (normally Fall, Winter, Spring/Summer, Fall) students must successfully complete ten halfcredit courses (four theoretical courses, three experimental/laboratory courses, one computational course, and two research seminar courses). In exceptional cases students may be able to finish the program in three terms of study. Theoretical courses PHYS 5P70 (Advanced Condensed Matter Physics); two of PHYS 5P11 (Theoretical Foundations of Materials Physics I), PHYS 5P30 (Advanced Electromagnetism), PHYS 5P41 (Advanced Statistical Physics), PHYS 5P50 (Advanced Quantum Mechanics I), PHYS 5P12 (Theoretical Foundations of Materials Physics II), PHYS 5P61 (Nuclear Physics), PHYS 5P62 (Modern Wave Optics); one of PHYS 5P74 (Magnetism & Magnetic Materials), PHYS 5P75 (Optical Properties of Solids), PHYS 5P76 (Nuclear Magnetic Resonance) Experimental/laboratory courses PHYS 5P81 (Sample Preparation and Characterization Techniques for Materials Science) PHYS 5P79 (Advanced Experimental Methods in Condensed Matter Physics I) PHYS 5P80 (Advanced Experimental Methods in Condensed Matter Physics II) Computational course PHYS 5P10 (Computational Methods for Materials Science) Research seminar courses PHYS 5P91 (Graduate Seminar I) PHYS 5P92 (Graduate Seminar II) PhD For fulltime students entering the PhD program through option 1 or 3, the program is normally a 12 term or four year program. For fulltime students entering the PhD program as a transfer student from the MSc, the program is normally a 15 term or five year program inclusive of the time spent in the MSc. All students must complete a research project that culminates in writing and defending a thesis. There will be an oral defence of the thesis. PhD students must enrol in the thesis course PHYS 7F90 each term. Students admitted through option 1 (with a completed MSc) and option 2 (transferring following completion of one year in the Brock MSc Physics program) must complete a total of 3.0 credits: two PHYS halfcredit courses at the 5(alpha)00 level or higher, PHYS 5P91 or PHYS 5P92, PHYS 7P91, PHYS 7F90 and PHYS 5N01. Additional credits may be required where a candidate is deficient in a particular area of study as determined by the supervisory committee. Three of the courses must be from Advanced Quantum Mechanics, Advanced Statistical Physics, Advanced Electrodynamics, Group Theory and Magnetism and Magnetic Materials unless already taken during the MSc studies (including equivalent courses from other institutions). Students admitted through option 3 (direct entry from a BSc) must complete a total of 4.0 credits: four PHYS halfcredit courses at the 5(alpha)00 level or higher (which must include three of the courses in Advanced Quantum Mechanics, Advanced Statistical Physics, Advanced Electrodynamics, Group Theory and Magnetism and Magnetic Materials), PHYS 5P91, PHYS 7P91, PHYS 7F90 and PHYS 5N01. Depending on their background and progress in the program, students may be required by the supervisory committee to take additional credits. Students must also successfully complete a comprehensive examination, which takes place within the first 24 months of the PhD program. Students must complete all of their course requirements (except the writing and the graduate seminar courses) before the comprehensive examination. Prior to the exam, the student must submit a written proposal of research. The examination committee consists of the Chair, two members of the supervisory committee and one additional Physics graduate faculty member. The examination consists of an oral presentation by the student about his/her research, followed by questions from the examination committee. The supervisor may attend but will not directly participate in the examination, however may provide confidential feedback on the student.  
Field(s) of Specialization (MSc, PhD)  
The department's main research emphasis is on condensed matter physics. The following research fields are currently represented, and are described in detail on our website at: http://www.physics.brocku.ca/Programs/  
Theoretical physics  
Superconductivity: unconventional pairing, novel materials (highTc, magnetic, etc.), localization and superconductivity, superconducting glassy state. Transport in metals: transport properties of heavy fermion systems. Noncrystalline materials: calculation of electronic structure and transport properties of amorphous and liquid metals, quasicrystals, alloys and semiconductors, vibrational and magnetic properties of amorphous solids. Linear response calculations of electronphonon interaction and superconductivity in solids. Quantum Monte Carlo studies of physical properties of isolated atoms and molecules. Monte Carlo and molecular dynamics studies of biological molecules. Dynamic systems. Mathematical physics.  
Experimental Condensed Matter Physics and Materials Science  
Investigation of the optical properties of materials with phase transitions (e.g., ferromagnets, superconductors, heavy fermion, spin and chargedensity wave compounds) via optical spectroscopy from mm wave to uv. Preparation and characterization of ceramic, single crystal and thin film (using pulsedlaser deposition) high Tc superconductors, CMR materials (manganites) and amorphous alloys. Magnetic and transport properties at ambient and high pressure utilizing measurement techniques such as SQUID magnetometry, specific heat and dcresistivity.  
Biophysics  
Nuclear Magnetic Resonance spectroscopy and relaxation measurements in soft condensed matter systems. Study of collective motions in model membranes, phase transitions in liquid crystals. Exploration of various morphologies and phase behaviour of lipid/water systems using scattering techniques (e.g. Neutrons, xray and light). Study of the protein/membrane interactions; structural characteristics of membrane active peptides. Biophysics of photosynthetic energy conversion using a combination of specialized optical spectroscopic techniques and theoretical models for excitation energy transfer and electron transport. Time resolved Electron Spin Resonance spectroscopy and lightinduced spin polarization in photosynthetic membrane proteins and donor acceptor molecular complexes. Investigation of energy and electron transfer and spin dynamics in these systems. Experimental research facilities are supported by electronics, glassblowing and machine shop services. The University provides extensive computing facilities using UNIX servers and highperformance clusters.  
Course Descriptions  
Note that not all courses are offered in every session. Refer to the applicable timetable for details. Students must check to ensure that prerequisites are met. Students may be deregistered, at the request of the instructor, from any course for which prerequisites and/or restrictions have not been met. PHYS 5F90 MSc Thesis An original research project involving the preparation and defence of a thesis which will demonstrate a capacity for independent work. The research shall be carried out under the supervision of a faculty member and the thesis defended at an oral examination. PHYS 5N01 Scientific Writing The organizational and stylistic skills of writing and referencing a scientific document. Examples from the various literature forms such as primary journals, reviews, reports, and theses, as well as presentations and seminars. Database use and reference citation, and use of figures and graphs to illustrate data. Note: This course is taught by instructors from Brock Student Development Centre. #PHYS 5P00 Quantum Chemistry: Theory (also offered as CHEM 5P00) Selfconsistentfield (SCF) method: configuration interaction; basis functions; electron correlation; physical properties of atoms, diatomic and polyatomic molecules. PHYS 5P02 Membrane Biophysics The structure of biological membranes, including their fluctuations, dynamics, and interactions. Lipids, their variety and purpose, especially for biotechnology. Membrane proteins, including introduction to ion channels and simple models of excitable membranes. Biophysical experimental methods for the study of membranes. #PHYS 5P09 Solitons and Nonlinear Wave Equations (also offered as MATH 5P09) Introduction to solitons: Linear and nonlinear travelling waves. Nonlinear evolution equations (Korteweg de Vries, nonlinear Schrodinger, sineGordon). Soliton solutions and their interaction properties. Lax pairs, inverse scattering, zerocurvature equations and Backlund transformations, Hamiltonian structures, conservation laws. Note: taught in conjunction with PHYS 4P09. *PHYS 5P10 Introduction to Scientific Computing (also offered as MATH 5P69) Survey of computational methods and techniques commonly used in condensed matter physics research; graphing and visualization of data; elements of programming and programming style; use of common subroutine libraries; common numerical tasks; symbolic computing systems. Case studies from various areas of computational physics. Disciplinespecific scientific writing and preparation of documents and presentations. Note: Taught in conjunction with PHYS 4P10 PHYS 5P11 Theoretical Foundations of Materials Physics I The foundations of thermal and statistical physics. Topics include heat and temperature, the kinetic theory of gases, laws of thermodynamics, entropy, thermodynamic functions and Maxwell's relations, equipartition of energy, partition functions, canonical and grand canonical ensembles and the chemical potential. Note: Students are required to complete an independent term project. Completion of this course will replace previous assigned grade and credit obtained in PHYS 5V85. PHYS 5P12 Theoretical Foundations of Materials Physics II A review of quantum mechanics: bound and scattering states, spin, atoms, periodic potentials. Crystal lattices: xray diffraction, electronic band structure. Review of classical and quantum statistics: electrons in metals and semiconductors, phonons, photons. Introduction to nonequilibrium and transport phenomena in materials. Note: Students are required to complete an independent term project. Completion of this course will replace previous assigned grade and credit obtained in PHYS 5V86. #PHYS 5P20 Computational Methods for Algebraic and Diffferential Systems (also offered as MATH 5P20) Computer algebra applications of solving polynomial systems of algebraic and differential systems of equations are covered, including the necessary algebraic background. Polynomials and ideals, Groebner bases, affine varieties, solving by elimination, Groebner bases conversion, solving equations by resultants, differential algebra, differential Groebner bases. PHYS 5P30 Advanced Electromagnetism Electromagnetic wave propagation in vacuum, dielectrics, conductors, and ionized gases; wave guide and transmission line propagation; dipole and quadrupole radiation fields; relativistic transformation of the electromagnetic fields; radiation by moving charges. PHYS 5P41 Advanced Statistical Physics Statistical ensembles; mean field and Landau theory, critical phenomena, and the renormalization group; quantum fluids; superfluidity; selected topics on disordered systems. PHYS 5P50 Advanced Quantum Mechanics I Angular momentum, rotations, and scalar and vector operators, selection rules; Pauli principle and periodic table; nuclear shell model; degenerate perturbation theory; electron in magnetic field, Landau levels; time evolution in quantum mechanics, timedependent perturbation theory; elastic scattering. PHYS 5P51 Advanced Quantum Mechanics II Propagators and Green's functions; path integral formalism; functional integrals and derivatives; systems of identical particles and second quantization; relativistic quantum mechanics. Prerequisite(s): PHYS 5P50 *PHYS 5P60 Partial Differential Equations (also offered as MATH 5P60) Review of linear and nonlinear equations in two variables. Existence and uniqueness theory, fundamental solutions, initial/boundaryvalue formulas for the heat equation, wave equation, Laplace equation in multidimensions. Exact solution techniques for 1st and 2nd order linear and nonlinear equations. Analysis of solutions, variational formulations, conservation laws, Noether's theorem. PHYS 5P61 Nuclear Physics Intrinsic properties of nuclei, nuclear binding energy; qualitative treatment of shell model; alpha, beta and gamma radioactivities, nuclear fission, characteristics of nuclear reactions. Note: course taught in conjunction with PHYS 4P61. PHYS 5P62 Modern Wave Optics: Optical Tweezers to Atom Clouds Optical lattices, spatial light modulators, evanescent waves and their applications from biology to ultracold atoms. Laser cooling and optical trapping. Manipulation of crystal properties by light. Optical patterns: tweezers, mirrors, funnels, bottles. Maple based course work. Note: course taught in conjunction with PHYS 4P62. #PHYS 5P64 Differential Geometry and Mathematical Physics (also offered as MATH 5P64) Topics may include: Lagrangian and Hamiltonian mechanics, field theory, differential geometric structures, Lie groups and Lie algebras, Gbundles, manifolds, introduction to algebraic topology. Applications to theoretical physics. PHYS 5P65 General Relativity Gravitation as a spacetime field theory. The spacetime metric, covariant derivative, and curvature; light cones and causality. Isolated systems and mass, energymomentum, angular momentum. Einstein's field equation of gravitation. Black hole solutions (Schwarzschild and Kerr metrics), cosmological solutions (RobertsonWalker metric), and their physical properties. #PHYS 5P66 Matrix groups and linear representations (also offered as MATH 5P66) Abelian groups, permutation groups, rotation groups. Representations of discrete and continuous groups by linear transformations (matrices). General properties and constructions of group representations. Representations of specific groups. Lie groups and Lie algebras. Applications in various areas of Mathematics, including invariant theory and group algebras, and Theoretical Physics, including crystallography and and symmetries in quantum systems. #PHYS 5P67 Biophysical Techniques (also offered as BIOL 5P67, BTEC 5P67 and CHEM 5P67) An advanced seminar/lecture course on experimental techniques in biophysics. The focus is on understanding the theory, applications and limitations of a variety of techniques students will encounter during their graduate studies. Techniques will range from advanced spectroscopy (absorption, fluorescence, NMR, Xray diffraction) to molecular biochemistry spectroscopy. #PHYS 5P68 Dynamical Systems (also offered as MATH 5P30) Introduction to dynamical systems and their applicatons in mathematical modeling. Linear flows, local theory of nonlinear flows, linearization theorems, stable manifold theorem. Global theory: limit sets and attractors, Poincare' Bendixson theorem. Structural stability and bifurcations of vector fields. Low dimensional phenomena in discrete dynamics. Chaotic dynamics: routes to chaos, characterization of chaos and strange attractors. PHYS 5P70 Advanced Condensed Matter Physics Energy bands in metals, semiconductors, and insulators; lattice dynamics; electrical, magnetic, thermal, optical, and transport properties of solids. PHYS 5P71 Special Topics in Condensed Matter Physics Longrange order in condensed matter systems: charge and spin density waves, etc; stronglycorrelated electron systems; quantum Hall effect; metalinsulator transitions; other topics to be selected by the instructor. PHYS 5P72 ManyBody Theory Green's functions at zero and finite temperature; perturbation theory and Feynman diagrams; linear response theory; electronelectron and electronphonon interactions; electrons in disordered systems; Fermi liquid theory; introduction to BCS theory of superconductivity. PHYS 5P73 Superconductivity I Overview of basic experimental facts; London theory; BCS theory; symmetry of the order parameter; GinzburgLandau theory and magnetic properties of superconductors; quasiparticle excitations in superconductors: thermal and transport properties; macroscopic phase coherence phenomena. PHYS 5P74 Magnetism and Magnetic Materials Fundamental and device applications of magnetism will be explored. Magnetic materials and magnetic measurements; domains, domain walls, domain processes, magnetization curves, and hysteresis; soft and hard magnetic materials and applications; magnetic recording; new developments and recent progress: magnetic multilayer structures, granular magnetic thin films, and giant magnetoresistance. PHYS 5P75 Optical Properties of Solids Measurement techniques; reflectivity, the dielectric function and the optical conductivity; LorentzDrude oscillator model; KramersKronig transformations and sum rules; properties of metals, insulators, and superconductors. PHYS 5P76 Nuclear Magnetic Resonance Density matrix formulation of NMR theory; spectroscopy of simple spin systems and spindependent interactions; relaxation theory; spin temperature; dipolar broadening in solids; NMR of soft condensed matter systems; practical aspects of highfidelity solidstate NMR; NMR spectrometer design; NMR imaging and microscopy. Prerequisite(s): PHYS 5P50 PHYS 5P77 Superconductivity II Fieldtheoretical methods in superconductivity. Gor'kov equations; strongcoupling theory; tunnelling; unconventional superconducting materials: hightemperature.superconductors, heavy fermion, magnetic, and organic superconductors. Prerequisite(s): PHYS 5P73 PHYS 5P78 Electronic Structure of Periodic and Aperiodic Systems Density Functional and related theories; survey of (semi)empirical and firstprinciples electronic structure methods; electronic structure of liquid metals, metallic glasses, random alloys, and quasicrystals; effective medium theories, coherent potential, and other approximations; recursion and other realspace methods. PHYS 5P79 Advanced Experimental Methods in Condensed Matter Physics Survey of experimental methods commonly used in condensed matter physics: optical and NMR spectroscopy, SQUID magnetometry, neutron and Xray scattering, lowtemperature and highpressure technology. The techniques presented will vary. Designing experiments with advanced equipment and critical analysis of the results on both statistical and methodological grounds. Introductory classroom centered section will be followed by several individualized handson modules of short duration focusing on each of the specific techniques. PHYS 5P80 Advanced Experimental Methods in Condensed Matter Physics II Continuation of classroom instruction and modules from PHYS 5P79 and/or new ones chosen from laser alignment, thin film deposition, vacuum technology, laser processing of materials, operation of class 100 clean rooms. PHYS 5P81 Sample Preparation and Characterization Techniques for Materials Science An experimental course that focuses on the synthesis of ceramic materials and fabrication of thin films of these materials. Nano particles of ceramic materials will be prepared by methods such as solgel and solidstate reactions. The structure and composition of the materials will be characterized by Xray, scanning electron microscope and energy dispersive Xray spectroscopy. The magnetic and electronic properties of the prepared materials will be characterized by various techniques learned in PHYS 5P79. Prerequisite(s): PHYS 5P79 or permission of the instructor. PHYS 5P91 Graduate Seminar I Independent study and presentation of major research papers in the area of specialization. Each student is required to attend and participate in all seminars given by students registered in the course. Students are also required to attend at least 80% of the Departmental seminars. PHYS 5P92 Graduate Seminar II Independent study and presentation of major research papers in the area of specialization. Each student is required to attend and participate in all seminars given by students registered in the course. Students are also required to attend at least 80% of the Departmental seminars. PHYS 5V805V89 Special Topics in Advanced Physics An investigation of a specific area or group of related topics in physics. Approval of the Graduate Program Director is required prior to registration. PHYS 7F90 PhD Thesis An original research project involving the preparation and defence of a thesis which will demonstrate a capacity for independent work. The research shall be carried out under the supervision of a faculty member and the thesis defended at an oral examination. PHYS 7P91 Graduate Seminar III Independent study and presentation of major research papers in the area of specialization. Each student is required to attend and participate in all seminars given by students registered in the course. Students are also required to attend at least 80% of the Departmental seminars.  
Last updated: July 11, 2019 @ 09:13AM