Non-Linear Forces and Irreversibility Problem in Classical Mechanics
... the material points are independent due to hypothesis of holonomic constraints [7,8]. Hence we arrive to the canonical Lagrange equations and to the principle of least action. Consequently, the scope of the canonical Lagrange equations and the principle of least action are determined by the generali ...
... the material points are independent due to hypothesis of holonomic constraints [7,8]. Hence we arrive to the canonical Lagrange equations and to the principle of least action. Consequently, the scope of the canonical Lagrange equations and the principle of least action are determined by the generali ...
ppt
... – But ‘character’ of motion remains the same. I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal. ...
... – But ‘character’ of motion remains the same. I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal. ...
Excitation Spectra of Circular, Few
... many-body states that are not included in the single-particle states of Eq. 1 (15). The S-T transition for N 5 2 is one such example (16). In Fig. 6A, E0,0 never crosses with E0,1, whereas in Fig. 6B a transition, labeled by the triangle, occurs between the first (dashed) excited state and (solid) g ...
... many-body states that are not included in the single-particle states of Eq. 1 (15). The S-T transition for N 5 2 is one such example (16). In Fig. 6A, E0,0 never crosses with E0,1, whereas in Fig. 6B a transition, labeled by the triangle, occurs between the first (dashed) excited state and (solid) g ...
Polymers on disordered trees, spin glasses, and traveling waves
... interest to study the directed polymer on a Cayley tree, which in some sense corresponds to a mean field limit d--, oe. On the Cayley tree we lose all spatial structure. Therefore (1.5) has to be replaced by energy fluctuations, which, however, have an exponent related to the roughness exponent by a ...
... interest to study the directed polymer on a Cayley tree, which in some sense corresponds to a mean field limit d--, oe. On the Cayley tree we lose all spatial structure. Therefore (1.5) has to be replaced by energy fluctuations, which, however, have an exponent related to the roughness exponent by a ...
Tailoring Optical Nonlinearities via the Purcell Effect
... 13), with a two-level system placed in the middle, as in Fig. 1. Note that the vast majority of PhC literature is generally focused on modification of dispersion relations at the frequency of the light that is sent in as a probe. By contrast, in the current work, it is only essential to modify th ...
... 13), with a two-level system placed in the middle, as in Fig. 1. Note that the vast majority of PhC literature is generally focused on modification of dispersion relations at the frequency of the light that is sent in as a probe. By contrast, in the current work, it is only essential to modify th ...
Publication : Relativistic Coupled Cluster Calculations with
... The quantum electrodynamic (QED) treatment of free elementary particles like the electron or the muon is now well established [1]. For example, the anomalous magnetic moment of the electron g − 2 can be determined precisely to ∼11 significant digits using summations over more than 10 000 terms of th ...
... The quantum electrodynamic (QED) treatment of free elementary particles like the electron or the muon is now well established [1]. For example, the anomalous magnetic moment of the electron g − 2 can be determined precisely to ∼11 significant digits using summations over more than 10 000 terms of th ...
Extrimes of Information Combining
... • The probability of spontaneous emission is always greater than 0 ...
... • The probability of spontaneous emission is always greater than 0 ...
The Detective`s Hat Function
... on the interval (0, 2) the curvature is so slight that the function appears to be linear) The slope of the tangent line at x = 0 is 2. ...
... on the interval (0, 2) the curvature is so slight that the function appears to be linear) The slope of the tangent line at x = 0 is 2. ...
Noninertial Frames
... Earth’s rotation) has a component ! z e z along the vertical at the specified latitude. If a particle is projected such that its velocity vector v r is located in the xy plane, then the Coriolis force will have a component directed to the right of the particle’s motion (see Figure 8-4). The size of ...
... Earth’s rotation) has a component ! z e z along the vertical at the specified latitude. If a particle is projected such that its velocity vector v r is located in the xy plane, then the Coriolis force will have a component directed to the right of the particle’s motion (see Figure 8-4). The size of ...
Quantum dissection of a covalent bond with the entanglement
... The values of λ for HF wave functions are listed in Table 1. We see that the perfectly localised groups of four (0, 0, 1, 1) and delocalised groups of two (1/2, 1/2) are the only grouping of electrons needed to describe most of the molecules. However, in the case of C2 and Be2 , there are groupings ...
... The values of λ for HF wave functions are listed in Table 1. We see that the perfectly localised groups of four (0, 0, 1, 1) and delocalised groups of two (1/2, 1/2) are the only grouping of electrons needed to describe most of the molecules. However, in the case of C2 and Be2 , there are groupings ...
PDF only - at www.arxiv.org.
... Everywhere in the variation region of the parameters V1,2 the first few terms provide the spectrum with the relative error of the order of or less than a few fractions of a percent. This conclusion states that the energy spectrum approximately obeys the functional dependence En ~ (n a0 a1 n1/3 ) ...
... Everywhere in the variation region of the parameters V1,2 the first few terms provide the spectrum with the relative error of the order of or less than a few fractions of a percent. This conclusion states that the energy spectrum approximately obeys the functional dependence En ~ (n a0 a1 n1/3 ) ...
Physical Review Letters 103, 233602 (2009)
... pulse (by a factor of 3 107 for our experimental parameters), and within the localized probe pulse region atoms are in the superposition state of Eq. (1) [2]. The probe laser field is thus mapped onto the atom wave function (shared by all atoms in the condensate), forming an ‘‘imprint’’ ( c 2 ) of ...
... pulse (by a factor of 3 107 for our experimental parameters), and within the localized probe pulse region atoms are in the superposition state of Eq. (1) [2]. The probe laser field is thus mapped onto the atom wave function (shared by all atoms in the condensate), forming an ‘‘imprint’’ ( c 2 ) of ...
The hydrogen atom as an entangled electron–proton system
... depends on the positions of the other particles, rather than on some average density. Consequently, in a system of interacting particles, the probability of finding two particles with given positions or momenta is not simply the product of the single-particle probabilities: We say that the particles ...
... depends on the positions of the other particles, rather than on some average density. Consequently, in a system of interacting particles, the probability of finding two particles with given positions or momenta is not simply the product of the single-particle probabilities: We say that the particles ...
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.