LECTURE NOTES ON STATISTICAL MECHANICS Scott Pratt Department of Physics and Astronomy
... to understand why all states are equally populated from the perspective of dynamics. The Ergodic theorem is built on the symmetry of time-reversal, i.e., the rate at which one changes from state i to state j is the same as the rate at which one changes from state j to state i. Here, we can consider ...
... to understand why all states are equally populated from the perspective of dynamics. The Ergodic theorem is built on the symmetry of time-reversal, i.e., the rate at which one changes from state i to state j is the same as the rate at which one changes from state j to state i. Here, we can consider ...
Minimal length scales for the existence of local temperature
... describe the approach to analyse its existence. Since temperature is defined to exist locally, i.e. for a given part of the system we consider, if the respective part is in a thermal equilibrium state, it is defined to exist on a certain length scale, if all possible partitions of the corresponding si ...
... describe the approach to analyse its existence. Since temperature is defined to exist locally, i.e. for a given part of the system we consider, if the respective part is in a thermal equilibrium state, it is defined to exist on a certain length scale, if all possible partitions of the corresponding si ...
rev1 - UConn Physics
... Problem 3 (correlated motion of 2 objects in 3-D) Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig. below. At the same time that the projectile leaves the cannon the target falls toward ground. Would the projectile now miss or hit the target ? ...
... Problem 3 (correlated motion of 2 objects in 3-D) Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig. below. At the same time that the projectile leaves the cannon the target falls toward ground. Would the projectile now miss or hit the target ? ...
Physics by analogy
... range from simple examples with superficial relations, often used to make a topic engaging and accessible to novices, to complex analogies with deep structural relations that are used to compare physical systems. The precise form that an analogy takes depends heavily on its function and the context o ...
... range from simple examples with superficial relations, often used to make a topic engaging and accessible to novices, to complex analogies with deep structural relations that are used to compare physical systems. The precise form that an analogy takes depends heavily on its function and the context o ...
Introduction to quantum Fisher information
... and the book [22] of Holevo. Although both the classical Cramér-Rao inequality and its quantum analog are mathematically as trivial as the Schwarz inequality, the subject takes a lot of attention because it is located on the boundary of statistics, information and quantum theory. As a starting poin ...
... and the book [22] of Holevo. Although both the classical Cramér-Rao inequality and its quantum analog are mathematically as trivial as the Schwarz inequality, the subject takes a lot of attention because it is located on the boundary of statistics, information and quantum theory. As a starting poin ...
Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
... With the subsequent development of physics, more compelling reasons emerged for questioning the continuum, including the singularities and infinities of General Relativity, of Quantum Field Theory (including the standard model), and of black hole thermodynamics. Einstein, for example, voiced doubts ...
... With the subsequent development of physics, more compelling reasons emerged for questioning the continuum, including the singularities and infinities of General Relativity, of Quantum Field Theory (including the standard model), and of black hole thermodynamics. Einstein, for example, voiced doubts ...
... these times. In contrast, the fastest firing neurons work on millisecond timescales, and polarization excitations in even the shortest microtubules are of order 10–7 sec. Thus quantum-level events, in particular the superpositional coherences necessary for quantum computation, simply do not have the ...
High-Performance Computing and Quantum Processing - HPC-UA
... sustained by any envisioned super-computer platforms due to fundamental and technological limits. Advanced digital integrated circuits (ICs) are used to implement various distinct computers designs, organizations and architectures. Enormous progress was achieved in semiconductor devices and ICs. The ...
... sustained by any envisioned super-computer platforms due to fundamental and technological limits. Advanced digital integrated circuits (ICs) are used to implement various distinct computers designs, organizations and architectures. Enormous progress was achieved in semiconductor devices and ICs. The ...
Quantum computation, non-demolition measurements, and reflective
... that it is possible to perform computation is such a way that expenditure of energy will be less than kT. The former should be true for the classical systems, while for details of quantum computers embodied into macromolecules it could consume as low as an order of kT(τ /τ ∗ ) of energy. The minim ...
... that it is possible to perform computation is such a way that expenditure of energy will be less than kT. The former should be true for the classical systems, while for details of quantum computers embodied into macromolecules it could consume as low as an order of kT(τ /τ ∗ ) of energy. The minim ...
The quantum system - Università degli Studi dell`Insubria
... eigenfunctions which differ only in the direction of k. The eigenfunctions within each subset are said to be degenerate, i. e., they have the same energy but differ in one or more of the eigenvalues needed to completely determine the state of the system. Looking at eq 2, we also see that decreasing ...
... eigenfunctions which differ only in the direction of k. The eigenfunctions within each subset are said to be degenerate, i. e., they have the same energy but differ in one or more of the eigenvalues needed to completely determine the state of the system. Looking at eq 2, we also see that decreasing ...
Elastic Collisions Momentum is conserved m 1 ѵ 1i +
... Inelastic – Think of these as ‘not’ bouncing. In fact, inelastic collisions occur when objects collide and stick together. ...
... Inelastic – Think of these as ‘not’ bouncing. In fact, inelastic collisions occur when objects collide and stick together. ...
On-site correlations in optical lattices: Band mixing
... provide a close connection between solid-state systems and atomic physics [1]. The models used to describe these systems generally assume that each lattice site’s wave function is easily built up from single-particle states [2]. Here we argue that this approximation is inappropriate for quantitative ...
... provide a close connection between solid-state systems and atomic physics [1]. The models used to describe these systems generally assume that each lattice site’s wave function is easily built up from single-particle states [2]. Here we argue that this approximation is inappropriate for quantitative ...
Magnetism: Models and Mechanisms - cond
... integrals. The label m indicates here the orbital quantum number of the Wannier function. In general the Hamiltonian (5) will include states stemming from more than a single atomic shell. For example, in the case of strongly-correlated transition-metal oxides, the set {im} includes transition-metal ...
... integrals. The label m indicates here the orbital quantum number of the Wannier function. In general the Hamiltonian (5) will include states stemming from more than a single atomic shell. For example, in the case of strongly-correlated transition-metal oxides, the set {im} includes transition-metal ...
Radiocommunication Study Groups
... continuous atomic time scale based on TAI with simultaneous broadcasting these two reference timescales (current UTC and continuous atomic time scale) on equal basis. However, practical implementation of Methods A and B seems difficult due to: - in case of Method A the problems related to disseminat ...
... continuous atomic time scale based on TAI with simultaneous broadcasting these two reference timescales (current UTC and continuous atomic time scale) on equal basis. However, practical implementation of Methods A and B seems difficult due to: - in case of Method A the problems related to disseminat ...
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.