( ) New Faculty Jan Egedal-Pedersen
... the creation of new materials, e.g., photonic bandgap crystals, or various surface plasmon systems, whose optical properties are dramatically different than those of any naturally occurring material. For example, nanostructured materials which display diffraction-less propagation of light, exhibit ...
... the creation of new materials, e.g., photonic bandgap crystals, or various surface plasmon systems, whose optical properties are dramatically different than those of any naturally occurring material. For example, nanostructured materials which display diffraction-less propagation of light, exhibit ...
Orders / Phases of matter
... lead to product states (what kind of product states?) -all states with short-range entanglement belong to the same phase -symmetry protected topological order / phases belong to this class -examples are 1.) Haldane phase (spin-1-chain where edge states have spin-1/2=fractionalization), 2.) the AKLT ...
... lead to product states (what kind of product states?) -all states with short-range entanglement belong to the same phase -symmetry protected topological order / phases belong to this class -examples are 1.) Haldane phase (spin-1-chain where edge states have spin-1/2=fractionalization), 2.) the AKLT ...
Assignment 4
... and the time B until the first bus is independent with Exponential(3) distribution. (a) Write down the joint probability density function of T and B. (b) Find the probability that the first taxi arrives before the first bus. (c) If you arrive at noon and take the first bus or taxi (whichever arrives ...
... and the time B until the first bus is independent with Exponential(3) distribution. (a) Write down the joint probability density function of T and B. (b) Find the probability that the first taxi arrives before the first bus. (c) If you arrive at noon and take the first bus or taxi (whichever arrives ...
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... successively decimated out and other couplings/fields are replaced by weaker ones generated by a perturbation calculation. During the RG procedure one keeps track of the energy scale, Ω, which is the actual value of the strongest coupling/transverse field; the average length scale, ξ, which is the c ...
... successively decimated out and other couplings/fields are replaced by weaker ones generated by a perturbation calculation. During the RG procedure one keeps track of the energy scale, Ω, which is the actual value of the strongest coupling/transverse field; the average length scale, ξ, which is the c ...
Differential Equations
... equation of heat conduction (1), we have v''(x) = 0, 0 < x < L. (5) Hence the steady-state temperature distribution is a linear function of x. Further v(x) must satisfy the boundary conditions v(0) = T1, v(L) = T2, (6) which are valid even as t →∞. The solution of Eq. (5) satisfying Eqs. (6) is v(x) ...
... equation of heat conduction (1), we have v''(x) = 0, 0 < x < L. (5) Hence the steady-state temperature distribution is a linear function of x. Further v(x) must satisfy the boundary conditions v(0) = T1, v(L) = T2, (6) which are valid even as t →∞. The solution of Eq. (5) satisfying Eqs. (6) is v(x) ...
2 Statistical Mechanics of Non-Interacting Particles
... Particles undergoing interaction with an external field, as opposed to with each other, also behave independently. The phase space expressions from the previous section are again important here, as long as the external potential does not confine the particles to such small volumes that the uncertain ...
... Particles undergoing interaction with an external field, as opposed to with each other, also behave independently. The phase space expressions from the previous section are again important here, as long as the external potential does not confine the particles to such small volumes that the uncertain ...
Quantum statistics: Is there an effective fermion repulsion or boson
... The quantity inside the curly brackets is the partition function for two quantum particles. The first term is the classical partition function, and its contribution already is accounted for in the classical ideal gas pressure; it cancels out in Eq. 共13兲. The second term corrects the incorrect classi ...
... The quantity inside the curly brackets is the partition function for two quantum particles. The first term is the classical partition function, and its contribution already is accounted for in the classical ideal gas pressure; it cancels out in Eq. 共13兲. The second term corrects the incorrect classi ...
webjune
... An approximate solution of the Thomas-Fermi equation for positive ions in a high magnetic field is obtained by making use of the variational principle. The radial wavefunctions of the hydrogen-like atom are used as the trial function that contains some variational parameters and satisfies the approp ...
... An approximate solution of the Thomas-Fermi equation for positive ions in a high magnetic field is obtained by making use of the variational principle. The radial wavefunctions of the hydrogen-like atom are used as the trial function that contains some variational parameters and satisfies the approp ...
Overall
... operators to represent the physical observables? What are the Hamiltonian and the Laplacian? What are an eigenvalue eqn., an eigenvalue, an eigenstate and a linear combination. What is the relationship between the Heisenberg uncertainty principle and operators? What are the Correspondence Principle ...
... operators to represent the physical observables? What are the Hamiltonian and the Laplacian? What are an eigenvalue eqn., an eigenvalue, an eigenstate and a linear combination. What is the relationship between the Heisenberg uncertainty principle and operators? What are the Correspondence Principle ...
Momentum and Impulse
... force is shown to be a function of time. The impulse is defined as the integral of the force over the time interval during which the force acts. It equals the total change in momentum of the particle. ...
... force is shown to be a function of time. The impulse is defined as the integral of the force over the time interval during which the force acts. It equals the total change in momentum of the particle. ...
particle in a box the uncertainty principle
... 3.8 Uncertainty Principle II -- derivation based on the particle properties of waves* I claimed above that the limits implied by the uncertainty principle are fundamental to nature, and are due to the wave properties of matter. This follows cleanly and logically from the mathematics of waves. As hu ...
... 3.8 Uncertainty Principle II -- derivation based on the particle properties of waves* I claimed above that the limits implied by the uncertainty principle are fundamental to nature, and are due to the wave properties of matter. This follows cleanly and logically from the mathematics of waves. As hu ...
Integrable Lattice Models From Gauge Theory
... The Yang-Baxter equation is a good example of a relationship that is much more transparent in terms of a picture (fig. 8) than by writing out an algebraic formula in detail. Actually, there is a subtle but important difference between the R-matrix that solves the YangBaxter equation and the S-matrix ...
... The Yang-Baxter equation is a good example of a relationship that is much more transparent in terms of a picture (fig. 8) than by writing out an algebraic formula in detail. Actually, there is a subtle but important difference between the R-matrix that solves the YangBaxter equation and the S-matrix ...
RESEARCH SUMMARIES
... charge carriers. The principal focus of the project is to elucidate the basic aspects of spin injection and propagation in different classes of magneto-electronic systems, ranging from conventional semiconductor quantum structures to hybrid ferromagnet/semiconductor bipolar devices and spanning dime ...
... charge carriers. The principal focus of the project is to elucidate the basic aspects of spin injection and propagation in different classes of magneto-electronic systems, ranging from conventional semiconductor quantum structures to hybrid ferromagnet/semiconductor bipolar devices and spanning dime ...
Momentum
... Momentum Momentum and changing momentum Momentum = mass x velocity (p = mv) Momentum is a vector quantity and is measured in Ns or kgms-1. ...
... Momentum Momentum and changing momentum Momentum = mass x velocity (p = mv) Momentum is a vector quantity and is measured in Ns or kgms-1. ...
01 introduction to quantum physics
... does not have a definite value for a quantity until it is observed. Thus an electron is given a specific spin by an observation; before this, it had only potential spins. A photon in the double slit interference experiment does not pass through a single slit unless we try to detect that slit passage ...
... does not have a definite value for a quantity until it is observed. Thus an electron is given a specific spin by an observation; before this, it had only potential spins. A photon in the double slit interference experiment does not pass through a single slit unless we try to detect that slit passage ...
Renormalization group
In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.