... The energy levels of hydrogenic atoms are mainly determined by their Dirac eigenvalues. However, the Breit correction on the Coulomb repulsion and QED effects such as radiative self-energy and vacuum polarization, incorporate non-negligible contributions, specially for highly ionized atoms as well a ...
Quantum fluctuations and thermodynamic processes in the presence of closed... by Tsunefumi Tanaka
... of these spacetimes is Grant space. It can be constructed from Minkowski space by im posing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking’s chronology protection conjecture is correct, there must be a physical mechanism preventing th ...
... of these spacetimes is Grant space. It can be constructed from Minkowski space by im posing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking’s chronology protection conjecture is correct, there must be a physical mechanism preventing th ...
Isotopic fractionation in proteins as a measure of hydrogen bond
... this simple model to hydrogen bonds in proteins, which are certainly complex and diverse chemical systems. First, our focus is on a small (but potentially important) sub-class of hydrogen bonds: short strong bonds. Second, we consider the simplest possible model that might capture the essential feat ...
... this simple model to hydrogen bonds in proteins, which are certainly complex and diverse chemical systems. First, our focus is on a small (but potentially important) sub-class of hydrogen bonds: short strong bonds. Second, we consider the simplest possible model that might capture the essential feat ...
Accuracy of microwave cavity perturbation measurements
... the integrand multiplied by the volume of the perturber. Equation (15) becomes ...
... the integrand multiplied by the volume of the perturber. Equation (15) becomes ...
Chirality quantum phase transition in the Dirac oscillator - E
... where 兩⌿典 is a two-component spinor which mixes spin-up and -down components with positive and negative energies. Remarkably enough, the Dirac oscillator coupling endows the particle with an intrinsic left-handed chirality which is only present in this two-dimensional scenario 关10兴. Conversely, the ...
... where 兩⌿典 is a two-component spinor which mixes spin-up and -down components with positive and negative energies. Remarkably enough, the Dirac oscillator coupling endows the particle with an intrinsic left-handed chirality which is only present in this two-dimensional scenario 关10兴. Conversely, the ...
Dielectrophoretic Growth of Metallic Nanowires
... (being built from ions). It has been shown that nanowires as thin as 5-10 nm could be made from the aqueous metal salt solution.14 Thus far, there has been no clear understanding of the growth process of metallic nanowires from its aqueous salt solution. In this article, we present experimental resu ...
... (being built from ions). It has been shown that nanowires as thin as 5-10 nm could be made from the aqueous metal salt solution.14 Thus far, there has been no clear understanding of the growth process of metallic nanowires from its aqueous salt solution. In this article, we present experimental resu ...
10.3 The Electric Field
... two bodies separated by some distance exert forces on each other, without ever coming into contact. There are other examples of “action at a distance” forces – namely the gravitational force between two masses, and the magnetic force between the north and south poles of bar magnets. Before the ninet ...
... two bodies separated by some distance exert forces on each other, without ever coming into contact. There are other examples of “action at a distance” forces – namely the gravitational force between two masses, and the magnetic force between the north and south poles of bar magnets. Before the ninet ...
Entropy, Strings, and Partitions of Integers
... Therefore, the state of a quantum string is specified by a sequence ψ of non-negative integers, ψ = (n1 , n2 , n3 , . . . ) , where n` is the state number of the oscillator with frequency `ω. The total energy of a string in state ψ is the sum of the energies in each of the individual oscillators, E ...
... Therefore, the state of a quantum string is specified by a sequence ψ of non-negative integers, ψ = (n1 , n2 , n3 , . . . ) , where n` is the state number of the oscillator with frequency `ω. The total energy of a string in state ψ is the sum of the energies in each of the individual oscillators, E ...
Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.In fact, ""Casimir's original goal was to compute the van der Waals force between polarizable molecules"" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas illustrate the Casimir force.