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
Peter Berg
Faculty of Mathematics and Science
Associate Dean
Melanie Pilkington
Faculty of Mathematics and Science
Core Faculty
Professors
Stephen Anco (Mathematics), Peter Berg (Physics), David A. Crandles (Physics), Thad A. Harroun (Physics), Alexandre Odesskii (Mathematics), Fereidoon S. Razavi (Physics), Maureen Reedyk (Physics), Kirill Samokhin (Physics), Thomas Wolf (Mathematics), Tony Yan (Chemistry)
Associate Professor
Edward Sternin (Physics), Amir Mofidi (Engineering)
Assistant Professors
Gavin Hester (Physics), Jasneet Kaur (Physics), Ganesh Ramachandran (Physics), Pouria Ramazi (Mathematics and Statistics), Barak Shoshany (Physics), Alonso Zavafer (Biology and Engineering)
Adjunct Professors
Tapash Chakraborty (University of Manitoba), Josef Dubicki (Hamilton Health Sciences), John Katsaras (NRC, Chalk River), Reinhard Kremer (MaxPlanck Institute, Germany), Jerry Sokolowski (University of Windsor)
Professors Emeriti
John E. Black (Physics), Shyamal K. Bose (Physics), Bozidar Mitrovic (Physics), Stuart M. Rothstein (Chemistry)
Graduate Program Director
Maureen Reedyk
mreedyk@brocku.ca
Administrative Assistant
Courtney Lee
9056885550, extension 3412
Mackenzie Chown B210
physics@brocku.ca
Graduate Administrative Coordinator
Elena Genkin
9056885550, extension 3115
Mackenzie Chown D473
egenkin@brocku.ca
Graduate Laboratory Supervisor
Sara Monafared
Senior Laboratory Supervisor
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 research 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 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 independently or in collaboration with others to fill jobs in industry, government agencies, research institutes and universities worldwide. The program offers two options: a 16month (four term) coursebased option and a 2year (six term) courseplusproject (MRP) option. Both options require completion of the noncredit Graduate Science Preparation seminar course PHYS 5N02 prior to or concurrent with the start of the program.
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 the business and societal impact of their work without prejudice. These goals will be achieved through graduate seminar presentations and through the production of detailed technical laboratory and term project 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 fouryear 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. 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 candidates.
Parttime candidates may be considered.
MSc in Materials Physics (ISP)
Successful completion of a fouryear 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 brocku.ca/nextstep/internationalstudents/englishlanguageproficiency/.
The Program Committee will review all applications and recommend admission for a limited number of candidates. Applicants holding a degree without sufficient background in Physics may be required to complete additional qualifying undergraduate courses prior to an admission decision.
All students in the program will be initially admitted to the coursebased option. Admission to the Major Research Project (MRP) option is on a competitive basis. Students may be admitted to the MRP option following completion of the first three terms of the MSMP (ISP) coursebased option. MRP students are required to maintain a minimum 75% overall average. Admission to the MRP option is on the basis of grades, and supervisor availability. An interview may be required. MRP students will complete all of the requirements for the MSMP coursebased program prior to starting the MRP. MRP students will normally complete the requirements of the MRP option over the two terms following completion of the MSMP coursebased program requirements.
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, except for 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 fouryear honours Bachelor's degree, or the equivalent; their academic standing and research potential must be demonstrably commensurate with readiness for doctoral study. 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 candidates.
Only fulltime PhD students will be admitted.


Degree Requirements 

Master of Science in Physics
Total Credits for the Program: 3.5
Required Courses:
Thesis:
Electives:

One additional PHYS 4*** or higher 0.5 Credit Courses 

Two additional PHYS 5*** or higher 0.5 Credit Courses 
Notes:
All students must complete a research project that culminates in writing and defending a thesis. 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. All students are also expected to attend Departmental seminars.
For fulltime students, the program is normally a six term or twoyear program.
*Requires permission of the graduate program director, and is intended for students who enter the program from a nontraditional background
MSc in Materials Physics (ISP)
Total Credits for the Program: 5.0 or 6.0 (Major Research Project option)
Requirements:
Graduate Science Preparation Seminar Course:
Theoretical Courses:
Experimental/Laboratory Courses:
Computational Course:
Research Seminar Course:
Research Project (Major Research Project option only)
Notes:
Students must successfully complete the program requirements over four terms of study (normally Fall, Winter, Spring/Summer, Fall). All students are also expected to attend Departmental seminars.
For fulltime students in the Major Research Project (MRP) option, the Materials Physics MSc is normally a six term or 24 month program. Every Materials Physics MSc MRP candidate must complete the course requirements of the coursebased program, and a fullcredit Research Project (PHYS 5P96 + PHYS 5P97). All candidates must conduct, submit, and present a Research Project which demonstrates proficiency in applying concepts in Materials Physics and is typically completed in the final two terms of study. In the penultimate term of the MRP option, students complete PHYS 5P96. In the final term of the MRP option, students complete PHYS 5P97.
PhD in Physics
Total Credits for the Program: 3.0 (students admitted with MSc or transfer from MSc), 4.0 (students admitted from BSc)
Required Courses:
Thesis:
Electives:

Three additional PHYS 5P** or higher 0.5 Credit Courses 

Two additional PHYS 5P** or higher 0.5 Credit Courses (students admitted from BSc only) 
Notes:
For fulltime students entering the PhD program through option 1 or 3, the program is normally a 12 term or fouryear program. For fulltime students entering the PhD program as a transfer student from the MSc, the program is normally a 15 term or fiveyear 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 defense of the thesis. PhD students must enroll in the thesis course PHYS 7F90 each term. All students are also expected to attend Departmental seminars.
All students must complete three courses from the following list during their graduate studies (Masters and Doctoral): Advanced Quantum Mechanics (PHYS 5P50), Advanced Statistical Physics (PHYS 5P41), Advanced Electrodynamics (PHYS 5P30), Group Theory (PHYS 5P66) and Magnetism and Magnetic Materials (PHYS 5P74). Equivalent courses from other institutions could be acceptable to satisfy this requirement upon approval by the Physics program at Brock University.
Additional credits may be required where a candidate is deficient in a particular area of study as determined by the supervisory committee.
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 course) before the comprehensive examination. The examination committee consists of a 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 their research, followed by questions from the examination committee. The supervisor may attend but will not directly participate in the examination.


Field(s) of Specialization 

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, highTc, magnetic, noncentrosymmetric superconductors, topological quantum materials, quantum magnets, topology in physics, dynamic systems, mathematical physics, general relativity, foundations of quantum mechanics, the nature of time and causality, time travel and fasterthanlight travel, symbolic and highperformance scientific computing, parallel and concurrent computing.


Experimental Condensed Matter Physics and Materials Science 

Investigation of the optical properties of materials via optical spectroscopy from mm wave to UV. Raman spectroscopy. Preparation and characterization of ceramic, single crystal and thin film (using pulsedlaser deposition) materials. Magnetic and transport properties at ambient and highpressure utilizing measurement techniques such as SQUID magnetometry, specific heat and dcresistivity. Synthesis, design, and investigation of nanostructured materials. Neutron scattering.


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. Computational methods in biomolecular simulations.
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 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
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
Organizational and stylistic skills of writing, referencing, and appropriate use of figures, graphs, and tables within an original scientific document such as a research journal article.
PHYS 5N02
Graduate Science Preparation Seminar
Intensive English seminar on the norms of the practice of science; the development of academic skills such as critical thinking and synthesizing arguments and ideas; referencing plagiarism; academic presentations and discussions; the development of specialized vocabulary in English.
Restriction: Students in the MSc in Materials Physics (ISP) Program, or permission of the instructor.
*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 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
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.
PHYS 5P12
Theoretical Foundations of Materials Physics II
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.
*PHYS 5P20
Computational Methods for Algebraic and Differential 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 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 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. 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)
Seminar/lecture course on experimental techniques in biophysics. 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 applications in mathematical modeling. Linear flows, local theory of nonlinear flows, linearization theorems, stable manifold theorem. Global theory: limit sets and attractors, Poincaré 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 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. 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
Experimental Methods in Materials Physics
Survey of experimental methods used in materials physics.
PHYS 5P81
Sample Preparation and Characterization Techniques for Materials Science
Experimental course that focuses on sample preparation. Projects may include the synthesis of ceramic materials and fabrication of thin films of these materials, nano particles of ceramic materials prepared by methods such as solgel and solidstate reactions, alloys and amorphous materials.
Prerequisite(s): PHYS 5P79 or permission of the instructor.
PHYS 5P82
Materials Physics Term Project
Culminating project investigating various structural, electronic, magnetic, and optical properties of materials prepared in PHYS 5P81 using various techniques learned in PHYS 5P79 and PHYS 5P80.
Prerequisite(s): PHYS 5P79, PHYS 5P80 and PHYS 5P81 or permission of the instructor.
PHYS 5P83
Foundations of Materials Physics Characterization
Introduction to the physics, theory of operation, and data analysis approaches of experimental materials physics characterization techniques.
Corequisite(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 all the Departmental seminars.
PHYS 5P92
Graduate Seminar in Materials Physics
Independent study and presentation of major research papers in materials physics. Each student is required to attend and participate in all seminars given by students registered in the course. Students are also required to attend all the Departmental seminars.
PHYS 5P96
Major Research Project in Materials Physics I
Comprehensive experimental, theoretical or computational research project in Materials Physics completed under the supervision of a faculty advisor. Literature review, project proposal and initial work.
Restriction: Open to MSMP students who have completed all of the course requirements for the coursebased MSMP Program option with permission of the Physics Graduate Program Director.
PHYS 5P97
Major Research Project in Materials Physics II
Comprehensive experimental, theoretical or computational research project in Materials Physics completed under the supervision of a faculty advisor. Project completion and report.
Restriction: Open to MSMP students who have completed all of the course requirements for the coursebased MSMP Program option with permission of the Physics Graduate Program Director.
Prerequisite(s): PHYS 5P96
#PHYS 5V50
Advanced Graduate Physics Theory
A first graduate course in the central theories of condensed matter physics. Topics include advanced electromagnetism, statistical physics, and quantum mechanics.
PHYS 5V805V89
Special Topics in Advanced Physics
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
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 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 all of the Departmental seminars.


