Last updated: October 29, 2021 @ 10:40AM

S. Ejaz Ahmed

Faculty of Mathematics and Science

Cheryl McCormick

Faculty of Mathematics and Science

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)

Thad A. Harroun (Physics), Edward Sternin (Physics)

Barak Shoshany

Ady Abdellatif, Josef Dubicki, John Katsaras (NRC, Chalk River), Reinhard Kremer (Max-Planck Institute, Germany), Jerry Sokolowski, Ole Steuernagel (University of Hertfordshire, UK), Ranjini Tolakanahalli, Heping Xu

John E. Black (Physics), Stuart M. Rothstein (Chemistry), Ramesh C. Shukla (Physics)

Maureen Reedyk

Elizabeth Horvath

Elena Genkin

TBA

Ivana Komljenovic Metcalf

Fulvio (Phil) Boseglav

The Department of Physics offers thesis-based 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. Hands-on 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 Master of Science in Materials Physics (MSMP) International Student Program (ISP) that provides intensive, hands-on 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 program offers two options: a 16-month (four term) course-based option and a 2 year (six term) course-plus-project (MRP) option. Both options require participaton in the Graduate Science Preparation Program (GSPP) 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 non-technical 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.

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.

Part-time candidates may be considered.

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 full-time 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/english-language-proficiency/. 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.

All students in the program will be initially admitted to the course-based 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) course-based 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 course-based program prior to starting the MRP. MRP students will normally complete PHYS 5F95 over the two terms following completion of the MSMP course-based program requirements.

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 four-years 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 full-time PhD students will be admitted.

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 half-credits. These must be at the 5(alpha)00 level or above with the exception of one half-credit 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. All students are also expected to attend Departmental seminars.

For full-time students, the program is normally a six term or two year program.

Students accepted into the program are required to complete a four-week 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 half-credit courses (four theoretical courses, four experimental/laboratory courses, one computational course, and one research seminar course). All students are also expected to attend Departmental seminars.

For full-time 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 course-based program, and a PHYS 5F95 Project. All candidates must conduct, submit, and present a PHYS 5F95 project which demonstrates proficiency in applying concepts in Materials Physics. The project is typically completed in the final two terms of study.

PHYS 5P70 (Advanced Condensed Matter Physics); two of PHYS 5P11 (Theoretical Foundations of Materials Physics I), PHYS 5P12 (Theoretical Foundations of Materials Physics II), PHYS 5P30 (Advanced Electromagnetism), PHYS 5P41 (Advanced Statistical Physics), PHYS 5P50 (Advanced Quantum Mechanics I), 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)

PHYS 5P79 (Advanced Experimental Methods in Condensed Matter Physics I)

PHYS 5P80 (Advanced Experimental Methods in Condensed Matter Physics II)

PHYS 5P81 (Sample Preparation and Characterization Techniques for Materials Science)

PHYS 5P82 (Materials Physics Term Project)

PHYS 5P10 (Computational Methods for Materials Science)

PHYS 5P91 (Graduate Seminar I)

For full-time students entering the PhD program through option 1 or 3, the program is normally a 12 term or four year program. For full-time 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 enroll in the thesis course PHYS 7F90 each term. All students are also expected to attend Departmental seminars.

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 half-credit courses at the 5(alpha)00 level or higher, PHYS 5P91, PHYS 7P91, PHYS 7F90 and PHYS 5N01. Students admitted through option 1 (with a completed MSc) who have already completed PHYS 5P91 must replace it with another PHYS half-credit course at the 5(alpha)00 level or higher. 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(PHYS 5P50), Advanced Statistical Physics(PHYS 5P41), Advanced Electrodynamics(PHYS 5P30), Group Theory(PHYS 5P66) and Magnetism and Magnetic Materials(PHYS 5P74) 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 half-credit courses at the 5(alpha)00 level or higher (which must include three of the courses in 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)), 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.

The following research fields are currently represented, and are described in detail on our website at: http://www.physics.brocku.ca/Programs/

Superconductivity: unconventional pairing, novel materials (high-Tc, magnetic, etc.), localization and superconductivity, superconducting glassy state. Transport in metals: transport properties of heavy fermion systems. Linear response calculations of electron-phonon 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. General Relativity. Research on the boundary between mathematics and physics, focusing on mathematical, theoretical, computational, and philosophical aspects of general relativity, both classical and quantum, including the nature of time and causality and applications of scientific computing to general relativity.

Investigation of the optical properties of materials with phase transitions (e.g., ferromagnets, superconductors, heavy fermion, spin- and charge-density wave compounds) via optical spectroscopy from mm wave to uv. Preparation and characterization of ceramic, single crystal and thin film (using pulsed-laser 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 dc-resistivity.

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, x-ray 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 light-induced 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 high-performance clusters.

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

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 5F95

A comprehensive experimental, theoretical or computational research project in Materials Physics completed under the supervision of a faculty advisor.

Restriction: Open to MSMP students who have completed all of the course requirements for the course-based MSMP program option with permission of the Physics Graduate Program Director.

PHYS 5N01

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

(also offered as CHEM 5P00)

Self-consistent-field (SCF) method: configuration interaction; basis functions; electron correlation; physical properties of atoms, diatomic and polyatomic molecules.

PHYS 5P02

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

(also offered as MATH 5P09)

Introduction to solitons: Linear and nonlinear travelling waves. Nonlinear evolution equations (Korteweg de Vries, nonlinear Schrodinger, sine-Gordon). Soliton solutions and their interaction properties. Lax pairs, inverse scattering, zero-curvature equations and Backlund transformations, Hamiltonian structures, conservation laws.

Note: taught in conjunction with PHYS 4P09.

PHYS 5P10

(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. Discipline-specific scientific writing and preparation of documents and presentations.

Note: Taught in conjunction with PHYS 4P10

PHYS 5P11

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

A review of quantum mechanics: bound and scattering states, spin, atoms, periodic potentials. Crystal lattices: x-ray diffraction, electronic band structure. Review of classical and quantum statistics: electrons in metals and semiconductors, phonons, photons. Introduction to non-equilibrium 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

(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

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

Statistical ensembles; mean field and Landau theory, critical phenomena, and the renormalization group; quantum fluids; superfluidity; selected topics on disordered systems.

PHYS 5P50

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, time-dependent perturbation theory; elastic scattering.

PHYS 5P51

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

(also offered as MATH 5P60)

Review of linear and nonlinear equations in two variables. Existence and uniqueness theory, fundamental solutions, initial/boundary-value formulas for the heat equation, wave equation, Laplace equation in multi-dimensions. Exact solution techniques for 1st and 2nd order linear and nonlinear equations. Analysis of solutions, variational formulations, conservation laws, Noether's theorem.

PHYS 5P61

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

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

(also offered as MATH 5P64)

Topics may include: Lagrangian and Hamiltonian mechanics, field theory, differential geometric structures, Lie groups and Lie algebras, G-bundles, manifolds, introduction to algebraic topology. Applications to theoretical physics.

PHYS 5P65

Gravitation as a spacetime field theory. The spacetime metric, covariant derivative, and curvature; light cones and causality. Isolated systems and mass, energy-momentum, angular momentum. Einstein's field equation of gravitation. Black hole solutions (Schwarzschild and Kerr metrics), cosmological solutions (Robertson-Walker metric), and their physical properties.

PHYS 5P66

(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

(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, X-ray diffraction) to molecular biochemistry spectroscopy.

PHYS 5P68

(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

Energy bands in metals, semiconductors, and insulators; lattice dynamics; electrical, magnetic, thermal, optical, and transport properties of solids.

PHYS 5P71

Long-range order in condensed matter systems: charge and spin density waves, etc; strongly-correlated electron systems; quantum Hall effect; metal-insulator transitions; other topics to be selected by the instructor.

PHYS 5P72

Green's functions at zero and finite temperature; perturbation theory and Feynman diagrams; linear response theory; electron-electron and electron-phonon interactions; electrons in disordered systems; Fermi liquid theory; introduction to BCS theory of superconductivity.

PHYS 5P73

Overview of basic experimental facts; London theory; BCS theory; symmetry of the order parameter; Ginzburg-Landau theory and magnetic properties of superconductors; quasiparticle excitations in superconductors: thermal and transport properties; macroscopic phase coherence phenomena.

PHYS 5P74

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

Measurement techniques; reflectivity, the dielectric function and the optical conductivity; Lorentz-Drude oscillator model; Kramers-Kronig transformations and sum rules; properties of metals, insulators, and superconductors.

PHYS 5P76

Density matrix formulation of NMR theory; spectroscopy of simple spin systems and spin-dependent interactions; relaxation theory; spin temperature; dipolar broadening in solids; NMR of soft condensed matter systems; practical aspects of high-fidelity solid-state NMR; NMR spectrometer design; NMR imaging and microscopy.

Prerequisite(s): PHYS 5P50

PHYS 5P77

Field-theoretical methods in superconductivity. Gor'kov equations; strong-coupling theory; tunnelling; unconventional superconducting materials: high-temperature.superconductors, heavy fermion, magnetic, and organic superconductors.

Prerequisite(s): PHYS 5P73

PHYS 5P78

Density Functional and related theories; survey of (semi)empirical and first-principles 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 real-space methods.

PHYS 5P79

Survey of experimental methods commonly used in condensed matter physics: optical and NMR spectroscopy, SQUID magnetometry, neutron and X-ray scattering, low-temperature and high-pressure 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 hands-on modules of short duration focusing on each of the specific techniques.

PHYS 5P80

Continuation of class-room 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

An 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 sol-gel and solid-state reactions, alloys and amorphous materials.

Prerequisite(s): PHYS 5P79 or permission of the instructor.

PHYS 5P82

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 5P91

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.

PHYS 5P92

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.

PHYS 5V80-5V89

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

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

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.