review on the quantum spin Hall effect by Macijeko, Hughes, and
... an integer denoted as the TKNN number (6) or Chern number (7). The bulk topological invariant is in turn related to the number of stable gapless boundary states. In the integer QH state, the Chern number is equal to the number of stable gapless edge states and is also the value of the quantized Hall ...
... an integer denoted as the TKNN number (6) or Chern number (7). The bulk topological invariant is in turn related to the number of stable gapless boundary states. In the integer QH state, the Chern number is equal to the number of stable gapless edge states and is also the value of the quantized Hall ...
Spin Hamiltonians and Exchange interactions
... large and expensive magnets, and that a typical exchange constant is 10meV (often more). In particular, it is rarely possible to apply a field large enough to force a system into a nearly saturated state (all spins nearly parallel), if the spin-spin couplings favor some other state. Most generally, ...
... large and expensive magnets, and that a typical exchange constant is 10meV (often more). In particular, it is rarely possible to apply a field large enough to force a system into a nearly saturated state (all spins nearly parallel), if the spin-spin couplings favor some other state. Most generally, ...
From Quantum Gates to Quantum Learning
... yield that the qutrit is in one of the basis states, , , or . The probability that a measurement of a qutrit yields state is , state is , and state is . The sum of these probabilities is one. The absolute values are required since, in general, , and γ are complex quantities. Pairs of qutrits are ...
... yield that the qutrit is in one of the basis states, , , or . The probability that a measurement of a qutrit yields state is , state is , and state is . The sum of these probabilities is one. The absolute values are required since, in general, , and γ are complex quantities. Pairs of qutrits are ...
Class 4. Leverage, residuals and influence
... The studentized residuals are driven by the leave one out idea, which is the basis for much computationally intensive modern statistics. The leave one out idea is often called “jackknifing”. This “leave one out” residual can be used as a basis for judging the predictive ability of a model. Clearly t ...
... The studentized residuals are driven by the leave one out idea, which is the basis for much computationally intensive modern statistics. The leave one out idea is often called “jackknifing”. This “leave one out” residual can be used as a basis for judging the predictive ability of a model. Clearly t ...
When does a physical system compute?
... some notion of a mathematical computation, what does it mean to say that some physical system is ‘running’ a computation? If we want to use computational notions in physics, then what are the necessary and sufficient conditions under which we can say that a particular physical system is carrying out ...
... some notion of a mathematical computation, what does it mean to say that some physical system is ‘running’ a computation? If we want to use computational notions in physics, then what are the necessary and sufficient conditions under which we can say that a particular physical system is carrying out ...
Aspects of quantum information theory
... computers”, capable of handling otherwise untractable problems, has excited not only researchers from many different fields like physicists, mathematicians and computer scientists, but also a large public audience. On a practical level all these new visions are based on the ability to control the qu ...
... computers”, capable of handling otherwise untractable problems, has excited not only researchers from many different fields like physicists, mathematicians and computer scientists, but also a large public audience. On a practical level all these new visions are based on the ability to control the qu ...
Chapter 7 LINEAR MOMENTUM
... 16. Jeremy has it right. By momentum conservation, Micah needs to throw the balls forward if he wants to propel himself backward, but the balls need not strike any surface. You can also consider Newton’s third law and see that it is the force by the balls on Micah’s hand that pushes Micah backward. ...
... 16. Jeremy has it right. By momentum conservation, Micah needs to throw the balls forward if he wants to propel himself backward, but the balls need not strike any surface. You can also consider Newton’s third law and see that it is the force by the balls on Micah’s hand that pushes Micah backward. ...
Conclusive exclusion of quantum states
... system prepared according to one of two descriptions, χ1 or χ2 , and Bob’s task is to identify which preparation he has been given. Bob observes the system and will identify the wrong preparation with probability q. Note that 0 q 1/2, as Bob will always have the option of randomly guessing the d ...
... system prepared according to one of two descriptions, χ1 or χ2 , and Bob’s task is to identify which preparation he has been given. Bob observes the system and will identify the wrong preparation with probability q. Note that 0 q 1/2, as Bob will always have the option of randomly guessing the d ...
Presentation slides
... “Count” to get two point correlation function analytically Fourier transform to give dynamical structure factor S(k, ω) Throughout we use units with ~ = kB = 1 ...
... “Count” to get two point correlation function analytically Fourier transform to give dynamical structure factor S(k, ω) Throughout we use units with ~ = kB = 1 ...
Momentum - eAcademy
... momentum to impulse; the impulse acting on an object is equal to its change in momentum. Since F t m v and m v , then F t . Determine how to change the momentum of a baseball that is hit with a bat. There are various ways to change an object’s momentum. One way is to change t ...
... momentum to impulse; the impulse acting on an object is equal to its change in momentum. Since F t m v and m v , then F t . Determine how to change the momentum of a baseball that is hit with a bat. There are various ways to change an object’s momentum. One way is to change t ...
Electronic Transport in One-Dimensional - Goldhaber
... box. The data indicate a gate-induced transition between singlet and triplet ground states for the dot. (c) Magnetic field dependence of the conductance at the point marked by the white triangle in 4a (a,b) Magnetic field evolution of conductance versus bias voltage on the left (triplet) and right ( ...
... box. The data indicate a gate-induced transition between singlet and triplet ground states for the dot. (c) Magnetic field dependence of the conductance at the point marked by the white triangle in 4a (a,b) Magnetic field evolution of conductance versus bias voltage on the left (triplet) and right ( ...
(Super) Oscillator on CP (N) and Constant Magnetic Field
... The harmonic oscillator plays a distinguished role in theoretical and mathematical physics, due to its overcomplete symmetry group. The wide number of hidden symmetries provides the oscillator with unique properties, e.g. closed classical trajectories, the degeneracy of the quantum-mechanical energy ...
... The harmonic oscillator plays a distinguished role in theoretical and mathematical physics, due to its overcomplete symmetry group. The wide number of hidden symmetries provides the oscillator with unique properties, e.g. closed classical trajectories, the degeneracy of the quantum-mechanical energy ...
Grand Unified Models and Cosmology
... The hot big-bang cosmology predicts the expansion of the universe and the present abundances of the light-elements. Its best recent success is the predicted perfect black-body spectrum of the cosmic background radiation (CBR) measured by COBE (Cosmic Background Explorer Satellite) [15]. But in spite ...
... The hot big-bang cosmology predicts the expansion of the universe and the present abundances of the light-elements. Its best recent success is the predicted perfect black-body spectrum of the cosmic background radiation (CBR) measured by COBE (Cosmic Background Explorer Satellite) [15]. But in spite ...
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.