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LS coupling
LS coupling

... Others, such as the finite nuclear mass and volume, and the relativistic velocity correction, are not small compared to the other perturbations. However, as I will explain at the end, they are not involved in splitting otherwise degenerate levels and hence are not important for the picture we build ...
Methods of Statistical Spectroscopy as an Optimization
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... In the traditional approach, spectral properties of atoms and molecules are determined using quantum chemical methods. In this approach individual energy levels and the appropriate transition probabilities are evaluated with a high precision but even for a few energy levels the computational effort ...
Hwa-Tung Nieh
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... 3. Gauge field A is U(1) and  is a scalar 4. The dual CFT (quiver SU(N) gauge theory) is known for some ƒ 5. By tuning ƒ we can reproduce different phase transitions ...
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... of ferroelectricity and magnetism can be used, for example, to construct four-states memories. In order to calculate physical properties of these more complicated compounds it is first necessary to fully understand electronic properties of the basic compound, i.e., PbTe, and to prepare tools to carr ...
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... In the case of a small Cooper pair box, , it is convenient to introduce the basic of excess Cooper pair numbers, N The Hamiltonian reads as: ...
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... to quantum spins and higher multipoles with many interacting neighbors. A Kondo-type screening of each spin is proposed for systems with extreme quantum fluctuations but without conduction electrons. Ground-state properties are examined for an extended two-channel Kondo model where the Hilbert spac ...
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... We account for indistinguishability by dividing by N !. Why? There are N ! ways of arranging N atoms at N sites. If we count each one of those configurations as distinct then we would over-count the partition function by a factor of N !. The Heisenberg uncertainty principle states that ...
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... Fourier transform, a mathematical procedure for separating individual oscillations from complex combinations, is used to convert the FID (time domain) into the familiar spectrum (frequency domain). This is done by a computer, using suitable software (e.g. the Cooley-Tukey algorithm). Relaxation is t ...
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Introduction to Quantum Monte Carlo

... ♦ Original formulation based on local updates using Metropolis ♦ Cluster updates using the operator loop update (Sandvik 1999) ♦ Improved updates using directed loops (Syljuåsen and Sandvik 2002) ...
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... IRFP [21]. The ground state of the system is given by a set of ordered clusters in the same geometry as in the classical percolation model —only nearest neighboring sites are combined into a cluster. In this cluster structure, the block entropy, determined by the number of the clusters connecting th ...
SOLID-STATE PHYSICS 3, Winter 2008 O. Entin-Wohlman Conductivity and conductance
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... destroyed, quantum interference disappears. One expects the dephasing time to be infinite at zero temperature, and to decrease as the temperature is increased. We will therefore assume that we are considering very low temperatures, such that the time over which the particle retains its phase coheren ...
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Berry Phase
Berry Phase

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Ising model

The Ising model (/ˈaɪsɪŋ/; German: [ˈiːzɪŋ]), named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice, allowing each spin to interact with its neighbors. The model allows the identification of phase transitions, as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition.The Ising model was invented by the physicist Wilhelm Lenz (1920), who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model has no phase transition and was solved by Ising (1925) himself in his 1924 thesis. The two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by Lars Onsager (1944). It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.In dimensions greater than four, the phase transition of the Ising model is described by mean field theory.
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