Duality Theory of Weak Interaction
... are prohibited. The reason is that Aaµ is an SU (N1 )-tensor with tensor index a, and Gkµ is an SU (N2 )-tensor with tensor index k. The above combination violates PRI. This point of view clearly shows that the classical electroweak theory violates PRI. Hence the classical electroweak theory is only ...
... are prohibited. The reason is that Aaµ is an SU (N1 )-tensor with tensor index a, and Gkµ is an SU (N2 )-tensor with tensor index k. The above combination violates PRI. This point of view clearly shows that the classical electroweak theory violates PRI. Hence the classical electroweak theory is only ...
Analysis of radiation patterns of rectangular microstrip
... distance around the patch sides and can be replaced with the fields E a that are tangential to the substrate surface [6]. The four extended edge areas around the patch serve as the effective radiating apertures. The model on the right assumes that the substrate is truncated beyond the extent of the ...
... distance around the patch sides and can be replaced with the fields E a that are tangential to the substrate surface [6]. The four extended edge areas around the patch serve as the effective radiating apertures. The model on the right assumes that the substrate is truncated beyond the extent of the ...
Chapter 9 Angular Momentum Quantum Mechanical Angular
... angular momentum operators all commute, and any one of the angular momentum components to form a complete set of commuting observables. We choose L2 , which commutes with all three component operators, and Lz , which is the conventional choice of components. The requirement for a complete set of com ...
... angular momentum operators all commute, and any one of the angular momentum components to form a complete set of commuting observables. We choose L2 , which commutes with all three component operators, and Lz , which is the conventional choice of components. The requirement for a complete set of com ...
Quantum Mechanics (Part II)
... twentieth century, it was then realized that matter, by then universally thought to be made up of particles, sometimes behaved like a wave, confounding our intuitions about the working of the world, but also holding out the hope that since both matter and light exhibited this so-called wave-particle ...
... twentieth century, it was then realized that matter, by then universally thought to be made up of particles, sometimes behaved like a wave, confounding our intuitions about the working of the world, but also holding out the hope that since both matter and light exhibited this so-called wave-particle ...
Department of Physics, Chemistry and Biology Master’s Thesis Thomas Fransson
... the Hamiltonian is time-independent, a separation of variables yields the timeindependent Schrödinger equation, where the right-hand-side becomes the energy of the system, E, times the wave function. The many-particle wave function does not in itself represent an observable, i.e. an entity that can ...
... the Hamiltonian is time-independent, a separation of variables yields the timeindependent Schrödinger equation, where the right-hand-side becomes the energy of the system, E, times the wave function. The many-particle wave function does not in itself represent an observable, i.e. an entity that can ...
Closed-Form Expressions for the Matrix Exponential
... exp B = A, as shown by Dattoli, Mari and Torre [2]. These authors used essentially the same tools as we do here and presented some of the results that we will show below, but leaving them in an implicit form. The aforementioned authors belong to a group that has extensively dealt with our subject ma ...
... exp B = A, as shown by Dattoli, Mari and Torre [2]. These authors used essentially the same tools as we do here and presented some of the results that we will show below, but leaving them in an implicit form. The aforementioned authors belong to a group that has extensively dealt with our subject ma ...
Nonradiative electron and energy transfer. Explicit
... functions are exact up to second-order in the system–bath coupling, their analytical forms explicitly consist of a weighted sum of delta functions in the frequency domain. Practically, on the other hand, they are alternatively replaced by phenomenological expressions, like Debye’s, Ohmic spectral fu ...
... functions are exact up to second-order in the system–bath coupling, their analytical forms explicitly consist of a weighted sum of delta functions in the frequency domain. Practically, on the other hand, they are alternatively replaced by phenomenological expressions, like Debye’s, Ohmic spectral fu ...
Quantum discord and remote state preparation
... EjB ̺/pj is the density matrix after a positive operator valued measure (POVM) {EjB } has been performed on B. A slightly different definition of discord, based on geometric considerations, was given in Ref. [16]. There, discord was defined as the distance, as measured by the square norm in the Hilb ...
... EjB ̺/pj is the density matrix after a positive operator valued measure (POVM) {EjB } has been performed on B. A slightly different definition of discord, based on geometric considerations, was given in Ref. [16]. There, discord was defined as the distance, as measured by the square norm in the Hilb ...
Entanglement and Tunable Spin-Spin Couplings between Trapped
... gate operations (562 s), the entanglement fidelity degrades to 74(4)%, implying a single-gate fidelity of 98% exclusive of state preparation and detection errors. For N ¼ 3 ions, we set the trap frequencies to !z =2 ¼ 1:484 MHz, !1 =2 ¼ 3:952 MHz, !2 =2 ¼ 3:663 MHz, and !3 =2 ¼ 3:215 MHz, and c ...
... gate operations (562 s), the entanglement fidelity degrades to 74(4)%, implying a single-gate fidelity of 98% exclusive of state preparation and detection errors. For N ¼ 3 ions, we set the trap frequencies to !z =2 ¼ 1:484 MHz, !1 =2 ¼ 3:952 MHz, !2 =2 ¼ 3:663 MHz, and !3 =2 ¼ 3:215 MHz, and c ...
University of Toronto Strongly Repulsive Ultracold
... difficulty being largely due to the enormous dimension of the vector space in which the problem is expressed. While classical systems of N particles can be described as a 6N dimensional phase space, and uncorrelated quantum systems only require a 3 dimensional continuous Hilbert space that describes ...
... difficulty being largely due to the enormous dimension of the vector space in which the problem is expressed. While classical systems of N particles can be described as a 6N dimensional phase space, and uncorrelated quantum systems only require a 3 dimensional continuous Hilbert space that describes ...
A Bird`s-Eye View of Density
... solids in physics. First applications relevant for fields traditionally considered more distant from quantum mechanics, such as biology and mineralogy are beginning to appear. Superconductivity, atoms in the focus of strong laser pulses, relativistic effects in heavy elements and in atomic nuclei, c ...
... solids in physics. First applications relevant for fields traditionally considered more distant from quantum mechanics, such as biology and mineralogy are beginning to appear. Superconductivity, atoms in the focus of strong laser pulses, relativistic effects in heavy elements and in atomic nuclei, c ...
Time reversal and the symplectic symmetry of the electron spin.
... this situation is the “large N” expansion, which extracts the collective physics of the real world by mapping it onto a solvable universe where particles carry a very large number (N) of spin components. This is a kind of synthetic quantum mechanics where 1/N plays the role of Planck’s constant and ...
... this situation is the “large N” expansion, which extracts the collective physics of the real world by mapping it onto a solvable universe where particles carry a very large number (N) of spin components. This is a kind of synthetic quantum mechanics where 1/N plays the role of Planck’s constant and ...
Physics 231 Topic 3: Forces & Laws of Motion
... because its mass is largest c) the normal force on the green crate is largest because its size is largest d) the gravitational force acting on each of the crates is the same e) all of the above ...
... because its mass is largest c) the normal force on the green crate is largest because its size is largest d) the gravitational force acting on each of the crates is the same e) all of the above ...
Top Condensation as a Motivated Explanation of the Top Forward
... couplings, and can be exchanged in the t-channel to produce the observed AtF B . In top condensation, electroweak symmetry is dynamically broken, as in technicolor (and in QCD), through the formation of bound states. The difference from technicolor is that the condensate is made up of the top quark ...
... couplings, and can be exchanged in the t-channel to produce the observed AtF B . In top condensation, electroweak symmetry is dynamically broken, as in technicolor (and in QCD), through the formation of bound states. The difference from technicolor is that the condensate is made up of the top quark ...
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.