A Blochwave or Bloch state is the wavefunction of a particle (usually, an electron) placed in a periodic potential.
A corollary of this result is that the Bloch wavevector k is a conserved quantity in a crystalline system (modulo addition of reciprocal lattice vectors), and hence the group velocity of the wave is conserved.
The concept of the Bloch state was developed by Felix Bloch in 1928, to describe the conduction of electrons in crystalline solids.
This work resulted in Bloch's first paper and, as he later remarked, it was a forerunner of the paper by Weisskopf and Wigner on radiation damping and the natural line widths of spectral lines.
Incidentally, the wave solution that Felix discovered was a version of what was known in mathematics as Floquet's Theorem and had been used previously by physicists without realizing its full implications for the quantum mechanics of solids.
Bloch and London pointed out that it was necessary, on thermodynamic grounds, that the superconducting state required a minimum of the energy below the critical temperature but that at temperatures above that point a zero current state is more probable.
A wave pulse sent through this background sheds light on the mathematical description of an electron traversing a quasiperiodic crystal.
The traveling wave going through the quasiperiodic pattern is analogous to an electronwave traversing a quasiperiodic material.
The spacing between the wave peaks was not constant, as in a periodic wave, but varied quasiperiodically between two values, which were related to the spacings in the pattern on the pan's bottom.
focus.aps.org /story/v11/st11 (515 words)
4 Bloch wave method.(Site not responding. Last check: 2007-10-09)
The Blochwave method makes use of the Bloch theorem that states that a particular solution of the motion of the electron of total energy E in a periodic potential V(r) is of the form:
The unknown are the ch(j) and the wavevector k(j) of the Blochwave (j).
The Blochwave approach allows to use a simple test to check that enough reflections have been introduced into the calculation: one has to repeat the calculation with one more reflection and check that the change induced in the largest eigenvalue is smaller than a given maximum.
Abstracts(Site not responding. Last check: 2007-10-09)
Rayleigh-Bloch surface waves are acoustic or electromagnetic waves which propagate parallel to a two-dimensional diffraction grating and which are exponentially damped with distance from the grating.
A numerical method is described which enables the frequencies of the Rayleigh-Bloch waves to be determined as a function of $\beta$ for an arbitrary cylinder cross-section.
The implications for large forces due to incident waves on a large but finite number of such cylinders in the ocean is discussed.
Abstracts(Site not responding. Last check: 2007-10-09)
In this paper, surface waves in the presence of an infinite periodic array of obstacles of rectangular cross-section are considered.
Rayleigh-Bloch surface waves are described by a localised wave motion which does not propagate energy away from the array.
Finally strong numerical evidence is given for embedded Rayleigh-Bloch waves that exist a single family of rectangular cross-section above the second cut-off.
Rich mode structure with complimentary patterns of intensity for orthogonal polarizations of electromagnetic Blochwave is predicted.
D. Boiko, G. Guerrero, and E. Kapon, "Polarization Blochwaves in photonic crystals based on vertical cavity surface emitting laser arrays," Opt.
Boiko, G. Guerrero, and E. Kapon, “Blochwave states in photonic crystals based on VCSEL arrays,” in Proceedings of the 26-th International Conference on the Physics of Semiconductors 2002 (ICPS 2002), A.R. Long and J.H. Davies, ed.
Radiative Transport in a Periodic Structure - Bal, Fannjiang, Papanicolaou, Ryzhik (ResearchIndex)(Site not responding. Last check: 2007-10-09)
We use systematically the Wigner transform and the Blochwave expansion.
The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, while the scattering part by the random fluctuations.
Multiple scattering of surface waves on a randomly inhomogeneous surface was treated recently in [3] for scalar waves propagating on a...
It was not until the arrival of Swiss physicist Felix Bloch, however, in 1934, that physics research at Stanford truly caught fire.
A refugee from the Nazis, Bloch was only 28 years old when he answered David Webster's invitation to join the Stanford faculty.
Encouraged initially by Enrico Fermi to do experimental physics because, among other things, it was "fun," in 1938 Bloch (in collaboration with Luis Alvarez) made the first experimental measurement of the magnetic moment of the neutron, marking the beginning of the work for which he is perhaps best known.
Music for Ondes Martenot NAXOS 8.555779 [PCW]: Classical CD Reviews- October 2004 MusicWeb(UK)(Site not responding. Last check: 2007-10-09)
Ondes is French for "waves" and Maurice Martenot (1898-1980) was the Frenchman who invented the instrument.
Only in Thomas Bloch’s Formule is the ondes played solo, elsewhere it is combined with the orchestra, piano, percussion, woodwind, vocals and other electronic instruments.
This is described as a repetitive toccata and was written as an encore for one his recitals.
Before students can advance to the study of quantum mechanics, they must master a potential stumbling block - the physics of oscillations and waves.
While many treatments of this mathematically complex subject leave students confused, Ingram Bloch's new test offers an especially accessible introduction that fully explains requisite mathematical techniques in the...
BP is of one of the world's largest energy companies, providing its customers with fuel for transportation, energy for heat and light, retail services and petrochemicals for everyday items.
Amazon.com: Ondes Martenot: Music(Site not responding. Last check: 2007-10-09)
Rare instrument specialist Thomas Bloch is equally at home performing on the soundtrack of Amadeus, on stage with Radiohead, or at Milan’s La Scala (playing glass harmonica, cristal Baschet or ondes Martenot).
These at times surprising works are performed by Bloch and some of his fellow-composers, and also feature Phil Minton, Fernand Quattrocchi, the Pomeranian Quartet and the Paderewski Philharmonic Orchestra, among others.
The ondes Martenot is one of my favourite 20th century 'period instruments' and this disc is a wonderful introduction to this instrument.
Homogenization of Periodic Structures via Bloch Decomposition: SIAM Journal on Applied Mathematics Vol.
In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered.
Using Blochwave decomposition, a new proof of convergence is furnished.
Analytic Trajectories for Mobility Edges in the Anderson Model (ResearchIndex)(Site not responding. Last check: 2007-10-09)
Abstract: A basis of Blochwaves, distorted locally by the random potential, is introduced for electrons in the Anderson model.
Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent site-energies, and so take definite values rather than distributions of values.
The transformed Hamiltonian is ordered, and may be interpreted as an itinerant electron interacting with a spin on each site.
citeseer.ist.psu.edu /608494.html (296 words)
physics central physics in pictures - in synch - catch a quasiperiodic wave(Site not responding. Last check: 2007-10-09)
physics central physics in pictures - in synch - catch a quasiperiodic wave
Recent research strengthens this case by showing Bloch-like liquid surface waves in a pool with a quasiperiodic floor pattern.
Read more about this research at Physical Review Focus.
Energy Citations Database (ECD) Document #7234884 - Optical Blochwaves in a semiconductor photonic lattice
Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
Optical Blochwaves in a semiconductor photonic lattice
