146 results on '"Shigeji Fujita"'
Search Results
2. On Nernst’s Theorem and Compressibilities
- Author
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Akira Suzuki, Shigeji Fujita, and James R. McNabb
- Subjects
Physics ,Physics::General Physics ,media_common.quotation_subject ,Thermodynamics ,Second law of thermodynamics ,symbols.namesake ,symbols ,Compressibility ,Nernst equation ,Nernst heat theorem ,Carnot cycle ,Absolute zero ,Entropy (arrow of time) ,Third law of thermodynamics ,media_common - Abstract
The unattainability of the absolute zero of temperature is proved by using Carnot’s theorem. Hence this unattainability is distinct from the Planck-Fer-mi statement of the Third Law of Thermodynamics that the entropy vanishes at T=0. It is shown that the isothermal compressibility KT is in general larger than the adiabatic compressibility Ks and the difference KT − Ks vanishes in the low temperature limit.
- Published
- 2017
3. Electronic Band Structure of Graphene Based on the Rectangular 4-Atom Unit Cell
- Author
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Masashi Tanabe, Shigeji Fujita, and Akira Suzuki
- Subjects
010302 applied physics ,Physics ,Condensed matter physics ,Graphene ,Phonon ,Fermi energy ,01 natural sciences ,law.invention ,Brillouin zone ,Reciprocal lattice ,law ,0103 physical sciences ,Physics::Atomic and Molecular Clusters ,Wave vector ,010306 general physics ,Electronic band structure ,Bloch wave - Abstract
The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model; the π-band energy holds a linear dispersion (e−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.
- Published
- 2017
4. Quantum Theory of the Seebeck Coefficient in YBCO
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Materials science ,Seebeck coefficient ,Quantum mechanics ,InformationSystems_INFORMATIONSTORAGEANDRETRIEVAL ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) - Published
- 2019
5. Theory of the Half-integer Quantum Hall Effect in Graphene
- Author
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Shigeji Fujita and Akira Suzuki
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Physics and Astronomy (miscellaneous) ,Condensed matter physics ,Phonon ,Graphene ,General Mathematics ,Thermal Hall effect ,Fermi surface ,02 engineering and technology ,Electron ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,021001 nanoscience & nanotechnology ,01 natural sciences ,law.invention ,Quantum spin Hall effect ,law ,0103 physical sciences ,Half-integer ,010306 general physics ,0210 nano-technology - Abstract
The unusual quantum Hall effect (QHE) in graphene is described in terms of the composite (c-) bosons, which move with a linear dispersion relation. The “electron” (wave packet) moves easier in the direction [1 1 0 c-axis] ≡ [1 1 0] of the honeycomb lattice than perpendicular to it, while the “hole” moves easier in [0 0 1]. Since “electrons” and “holes” move in different channels, the particle densities can be high especially when the Fermi surface has “necks”. The strong QHE arises from the phonon exchange attraction in the neighborhood of the “neck” surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the superconducting energy gap caused by the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron–two-fluxons c-fermions by phonon-exchange attraction. The half-integer quantization rule for the Hall conductivity: (1/2)(2P−1)(4e 2/h), P=1,2,..., is derived.
- Published
- 2016
6. Lattice Stability and Reflection Symmetry
- Author
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James R. McNabb, Shigeji Fujita, Akira Suzuki, and Hung-Cheuk Ho
- Subjects
Physics ,Condensed matter physics ,business.industry ,Phonon ,Crystal structure ,Triclinic crystal system ,Condensed Matter::Materials Science ,Tetragonal crystal system ,Reflection symmetry ,Optics ,Condensed Matter::Superconductivity ,Crystal momentum ,Condensed Matter::Strongly Correlated Electrons ,Orthorhombic crystal system ,business ,Monoclinic crystal system - Abstract
Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional; no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.
- Published
- 2015
7. Electron Dynamics in Solids
- Author
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Akira Suzuki, Shigeji Fujita, and James R. McNabb
- Subjects
Physics ,Condensed matter physics ,Wave packet ,Dirac (software) ,Crystal system ,Fermi energy ,Wave vector ,Electron ,Triclinic crystal system ,Thermal conduction - Abstract
Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.
- Published
- 2015
8. On the Heisenberg and Schrödinger Pictures
- Author
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James MacNabb, Shigeji Fujita, and Akira Suzuki
- Subjects
Geometric quantization ,Physics ,symbols.namesake ,Pauli exclusion principle ,Fermionic field ,Interaction picture ,Quantum mechanics ,symbols ,Schrödinger picture ,Second quantization ,Heisenberg picture ,S-matrix - Abstract
A quantum theory for a one-electron system can be developed in either Heisenberg picture or Schrodinger picture. For a many-electron system, a theory must be developed in the Heisenberg picture, and the indistinguishability and Pauli’s exclusion principle must be incorporated. The hydrogen atom energy levels are obtained by solving the Schrodinger energy eigenvalue equation, which is the most significant result obtained in the Schrodinger picture. Both boson and fermion field equations are nonlinear in the presence of a pair interaction.
- Published
- 2014
9. Theory of Low- and High-Field Transports in Metallic Single-Wall Nanotubes
- Author
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Akira Suzuki, Hung-Cheuk Ho, and Shigeji Fujita
- Subjects
Free electron model ,Materials science ,Condensed matter physics ,Phonon ,Scattering ,law ,Electric field ,Supercurrent ,Carbon nanotube ,Ohmic contact ,Magnetic field ,law.invention - Abstract
Individual metallic single-wall carbon nanotubes show unusual non-Ohmic transport behaviors at low and high bias fields. For low-resistance contact samples, the differential conductance increases with increasing bias, reaching a maximum at ~100 mV. As the bias increases further, drops dramatically [1]. The higher the bias, the system behaves in a more normal (Ohmic) manner. This low-bias anomaly is temperature-dependent (50 - 150 K). We propose a new interpretation. Supercurrents run in the graphene wall below ~150 K. The normal hole currents run on the outer surface of the wall, which are subject to the scattering by phonons and impurities. The currents along the tube length generate circulating magnetic fields and eventually destroy the supercurrent in the wall at high enough bias, and restore the Ohmic behavior. If the prevalent ballistic electron model is adopted, then the temperature-dependent scattering effects cannot be discussed. For the high bias (0.3 - 5 V), (a) the I-V curves are temperature-independent (4 - 150 K), and (b) the currents (magnitudes) saturate. The behavior (a) arises from the fact that the neutral supercurrent below the critical temperature is not accelerated by the electric field. The behavior (b) is caused by the limitation of the number of quantum-states for the “holes” running outside of the tube.
- Published
- 2013
10. Theory of Seebeck Coefficient in Multi-Walled Carbon Nanotubes
- Author
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Shigeji Fujita, Akira Suzuki, and James R. McNabb
- Subjects
Superconductivity ,Condensed Matter::Materials Science ,Materials science ,Electromotive force ,Condensed matter physics ,Hall effect ,Condensed Matter::Superconductivity ,Seebeck coefficient ,Density of states ,Thermodynamics ,Fermi energy ,Cooper pair ,Thermoelectric materials - Abstract
Based on the idea that different temperatures generate different conduction electron densities and the resulting carrier diffusion generates the thermal electromotive force (emf), a new formula for the Seebeck coefficient (thermopower) S is obtained: S=(2/3)ln2(qn)-1eFkBD0, where kB is the Boltzmann constant, and q, n, eF, D0 are charge, carrier density, Fermi energy, density of states at eF, respectively. Ohmic and Seebeck currents are fundamentally different in nature, and hence, cause significantly different behaviors. For example, the Seebeck coefficient S in copper (Cu) is positive, while the Hall coefficient is negative. In general, the Einstein relation between the conductivity and the diffusion coefficient does not hold for a multicarrier metal. Multi-walled carbon nanotubes are superconductors. The Seebeck coefficient S is shown to be proportional to the temperature T above the superconducting temperature Tc based on the model of Cooper pairs as carriers. The S follows a temperature behavior, , where Tg ’= constant, at the lowest temperatures.
- Published
- 2013
11. Theory of Conductivity in Semiconducting Single-Wall Carbon Nanotubes
- Author
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Akira Suzuki, Salvador Godoy, and Shigeji Fujita
- Subjects
Materials science ,Condensed matter physics ,Graphene ,Phonon ,chemistry.chemical_element ,Electron ,Carbon nanotube ,Conductivity ,Thermal conduction ,law.invention ,chemistry ,law ,Cooper pair ,Carbon - Abstract
The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows “holes” (not “electrons”) to move inside the tube. This case accounts for a semiconducting behavior with the activation energy of the order of around 3 meV. There is a distribution of the activation energy since the pitch and the circumference can vary. Otherwise nanotubes show metallic behaviors (significantly higher conductivity). “Electrons” and “holes” can move in the graphene wall (two dimensions). The conduction in the wall is the same as in graphene if the finiteness of the circumference is disregarded. Cooper pairs formed by the phonon exchange attraction moving in the wall is shown to generate a temperature-independent conduction at low temperature (3 - 20 K).
- Published
- 2012
12. Theory of Zero-Resistance States Generated by Radiation in GaAs/AlGaAs
- Author
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Akira Suzuki, Shigeji Fujita, and Kei Ito
- Subjects
Condensed Matter::Quantum Gases ,Superconductivity ,Physics ,Condensed matter physics ,Field (physics) ,Band gap ,Electrical resistivity and conductivity ,Excited state ,Zero resistance ,Radiation ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Gaas algaas - Abstract
Mani observed zero-registance states similar to those quantum-Hall-effect states in GaAs/AlGaAs but without the Hall resistance plateaus upon the application of radiations [R. G. Mani, Physica E 22, 1 (2004)]. An interpretation is presented. The applied radiation excites “holes”. The condensed composite (c)-bosons formed in the excited channel create a superconducting state with an energy gap. The supercondensate suppresses the non-condensed c-bosons at the higher energy, but it cannot suppress the c-fermions in the base channel, and the small normal current accompanied by the Hall field yeilds a B-linear Hall resistivity.
- Published
- 2012
13. THEORY OF THE ELECTRICAL TRANSPORT IN METALLIC SINGLE-WALL NANOTUBES
- Author
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Akira Suzuki, Yoichi Takato, and Shigeji Fujita
- Subjects
Superconductivity ,Materials science ,Condensed matter physics ,Phonon scattering ,Phonon ,Graphene ,Statistical and Nonlinear Physics ,Carbon nanotube ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Condensed Matter Physics ,law.invention ,Condensed Matter::Materials Science ,law ,Ballistic conduction ,Ballistic conduction in single-walled carbon nanotubes ,Cooper pair - Abstract
A metallic (semiconducting) single-wall nanotube contains an irrational (integral) number of carbon hexagons in the pitch. The room-temperature conductivity is higher by two to three orders of magnitude in metallic nanotubes than in semiconducting nanotubes. Tans et al. [Nature386 (1997) 474] measured the electrical currents in metallic single-wall carbon nanotubes under bias and gate voltages, and observed non-Ohmic behaviors. The original authors interpreted their data in terms of a ballistic transport due to the Coulomb blockage on the electron-carrier model. The mystery of why a ballistic electron is not scattered by impurities and phonons is unexplained, however. An alternate interpretation is presented based on the Cooper pair (pairon)–carrier model. Superconducting states are generated by the Bose–Einstein condensation of the ± pairons at momenta 2πℏn/L, where L is the tube length and n a small integer. As the gate voltage changes the charging state of the tube, the superconducting states jump between different n. The normal current peak shapes appearing in the transition are found to be temperature-dependent, which is caused by the electron–optical phonon scattering.
- Published
- 2011
14. Theory of the anisotropic magnetoresistance in copper
- Author
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Akira Suzuki, Shigeji Fujita, Nebi Demez, and Yoichi Takato
- Subjects
Guiding center ,Magnetoresistance ,Condensed matter physics ,chemistry.chemical_element ,Fermi surface ,General Chemistry ,Electron ,Condensed Matter Physics ,Thermal conduction ,Copper ,Magnetic field ,chemistry ,Lattice (order) ,Condensed Matter::Strongly Correlated Electrons ,General Materials Science - Abstract
The motion of the guiding center of magnetic circulation generates a charge transport. The application of kinetic theory to the motion gives a modified Drude formula for the magnetoconductivity: σ = e 2 n c τ / M * , where M⁎ is the magnetotransport mass distinct from the cyclotron mass, nc the density of the conduction electrons, and τ the relaxation time. The density nc depends on the applied magnetic field direction relative to copper's face-centered-cubic lattice, when the Fermi surface of copper is nonspherical with necks. The anisotropic magnetoresistance of copper is calculated with the assumption of the necks representing by spheres of radius a centered at the eight singular points on the ideal Fermi surface. A good fit with experiments is obtained.
- Published
- 2010
15. MAGNETORESISTANCE IN COPPER
- Author
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Shigeji Fujita, Jeong-Hyuk Kim, H. C. Ho, and Nebi Demez
- Subjects
Physics ,Guiding center ,Condensed matter physics ,Magnetoresistance ,Cyclotron ,chemistry.chemical_element ,Statistical and Nonlinear Physics ,Fermi surface ,Electron ,Condensed Matter Physics ,Thermal conduction ,Copper ,Magnetic field ,law.invention ,chemistry ,law - Abstract
The motion of the guiding center of magnetic circulation generates a charge transport. By applying kinetic theory to the guiding center motion, an expression for the magnetoconductivity σ is obtained: σ = e2ncτ/M*, where M* is the magnetotransport mass distinct from the cyclotron mass, nc the density of the conduction electrons, and τ the relaxation time. The density nc depends on the magnetic field direction relative to copper's fcc lattice, when Cu's Fermi surface is nonspherical with “necks”. The anisotropic magnetoresistance is analyzed based on a one-parameter model, and compared with experiments. A good fit is obtained.
- Published
- 2008
16. THEORY OF THE FERMIONIC QUANTUM HALL EFFECT
- Author
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J. Hajdu, Y. Okamura, and Shigeji Fujita
- Subjects
Physics ,Field (physics) ,Quantum spin Hall effect ,Condensed matter physics ,Physical constant ,Filling factor ,Quantum mechanics ,Composite fermion ,Statistical and Nonlinear Physics ,Electron ,Fermion ,Quantum Hall effect ,Condensed Matter Physics - Abstract
At the even-denominator filling factor ν=P/Q, even Q, a fermionic Quantum Hall (QH) state is shown to be developed at the lowest temperatures. In this state, formed by the composite (c-) fermions, each with an electron and the even number Q of flux quanta (fluxons), the conductivity σ≡J/E(J= current density , E= applied field ) becomes a universal constant (e2/h)Q-2 as the temperature T approaches zero while the Hall conductivity σH≡J/EH(EH= Hall field ) becomes approximately equal to (e2/h)(P/Q).
- Published
- 2003
17. Quantum Hall Effect
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Physics ,Quantum spin Hall effect ,Condensed matter physics ,Quantum mechanics ,Composite fermion ,Quantum oscillations ,Landau quantization ,Quantum Hall effect - Published
- 2014
18. Magnetic Oscillations
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Physics ,Condensed matter physics - Published
- 2014
19. Phonons and Electron-Phonon Interaction
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Physics ,Lattice dynamics ,Superconductivity ,Condensed matter physics ,Phonon ,Quantum mechanics ,Van Hove singularity ,Electron phonon - Published
- 2014
20. Metallic (or Superconducting) SWNTs
- Author
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Shigeji Fujita and Akira Suzuki
- Subjects
Metal ,Superconductivity ,Materials science ,Condensed matter physics ,law ,Graphene ,visual_art ,visual_art.visual_art_medium ,Bose–Einstein condensate ,law.invention - Published
- 2014
21. Kinetic Theory and the Boltzmann Equation
- Author
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Shigeji Fujita and Akira Suzuki
- Subjects
Physics ,symbols.namesake ,Boltzmann relation ,Classical mechanics ,Boltzmann constant ,Kinetic theory of gases ,symbols ,Lattice Boltzmann methods ,Statistical physics ,Direct simulation Monte Carlo ,Poisson–Boltzmann equation ,Boltzmann equation ,Maxwell–Boltzmann distribution - Published
- 2014
22. Electrical Conductivity of Multiwalled Nanotubes
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Optical properties of carbon nanotubes ,Materials science ,Electrical resistivity and conductivity ,Graphene ,law ,Selective chemistry of single-walled nanotubes ,Ballistic conduction in single-walled carbon nanotubes ,Mechanical properties of carbon nanotubes ,Composite material ,law.invention - Published
- 2014
23. Quantum Hall Effect in Graphene
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Physics ,Quantum spin Hall effect ,Condensed matter physics ,Graphene ,law ,Quantum mechanics ,Composite fermion ,Electron ,Quantum Hall effect ,Bilayer graphene ,Graphene nanoribbons ,law.invention - Published
- 2014
24. Magnetic Susceptibility
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Nuclear magnetic resonance ,Materials science ,Magnetic susceptibility - Published
- 2014
25. Seebeck Coefficient in Multiwalled Carbon Nanotubes
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Metal ,Conduction electron ,Materials science ,Condensed matter physics ,Graphene ,law ,visual_art ,Seebeck coefficient ,visual_art.visual_art_medium ,Ballistic conduction in single-walled carbon nanotubes ,Multiwalled carbon ,law.invention - Published
- 2014
26. Three-dimensional transmission coefficients for neutrons and photons in amorphous materials
- Author
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Shigeji Fujita and Salvador Godoy
- Subjects
Physics ,Photon ,Condensed matter physics ,Neutron diffraction ,General Physics and Astronomy ,Boltzmann equation ,Amorphous solid ,symbols.namesake ,Boltzmann constant ,symbols ,Transmission coefficient ,Physical and Theoretical Chemistry ,Diffusion (business) ,Convection–diffusion equation - Abstract
We use Boltzmann’s transport equation to calculate the 3D incoherent Landauer equation for neutrons and photons diffusing in a slab of amorphous material. We use the P1 approximation to calculate the multiple-scattering transmission coefficient as a function of the diffusion coefficient. The 3D transmission coefficient obtained is smaller than the 1D case. The P1 result, valid only for thick slabs, is proved to be an excellent approximation to the exact solution.
- Published
- 2001
27. MICROSCOPIC THEORY OF THE QUANTUM HALL EFFECT
- Author
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Akira Suzuki, Shigeji Fujita, and Yoshiyasu Tamura
- Subjects
Physics ,Fluxon ,Condensed matter physics ,Phonon ,Degenerate energy levels ,Statistical and Nonlinear Physics ,Electron ,Quantum Hall effect ,Microscopic theory ,Condensed Matter Physics ,Plateau (mathematics) ,Boson - Abstract
The phonon exchange between the electron and the elementary magnetic flux (fluxon) induces an attractive transition in the degenerate Landau states. This attraction bounds an electron–fluxon complex. The center-of-mass of the complex moves as a boson with a linear dispersion relation (∊ = cp). The 2D system of free massless bosons undergoes a Bose–Einstein condensation at k B T c = 1.954ℏcn1/2, where n is the boson density. For GaAs/AlGaAs, T c ~ 1 K at the principal Landau-level occupation ratio ν = 1, where the electron number equals the fluxon number. Below T c , there is an energy gap, which stabilizes the Hall resistivity plateau. The plateau value (j/N)(h/e2) at the fractional occupation ratio ν = N/j, for odd j, indicates that the composite boson containing an electron and j fluxons carries the fractional charge (magnitude) e/j due to the magnetic confinement.
- Published
- 2001
28. ON THE OUT-OF-PLANE MAGNETOTRANSPORT IN <font>YBa</font>2<font>Cu</font>3<font>O</font>y
- Author
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Akira Suzuki, Yoshiyasu Tamura, and Shigeji Fujita
- Subjects
Physics ,Range (particle radiation) ,Condensed matter physics ,chemistry.chemical_element ,Statistical and Nonlinear Physics ,Electron ,Atmospheric temperature range ,Condensed Matter Physics ,Copper ,Out of plane ,chemistry ,Electrical resistivity and conductivity ,Charge carrier ,Quantum tunnelling - Abstract
The out-of-plane resistivity, ρc, in a single-crystal YBa 2 Cu 3 O y follows the experimental law: ρc=C1ρab+C2/T, where C1, C2 are the constants and ρab is in-plane resistivity in the concentration range 6.6 c , 90 K, occurring at y=6.88 and in the temperature range T c 2/T arises from the quantum tunneling between copper planes of the – pairons, moving with a linear dispersion relation, and the first term C1ρab from the in-plane currents due to the "holes" and +pairons.
- Published
- 2000
29. ON THE SUSCEPTIBILITY IN <font>La</font>2-x<font>Sr</font>x<font>CuO</font>4
- Author
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Shigeji Fujita, Yoshinobu Okamura, and Tsunehiro Obata
- Subjects
Physics ,Range (particle radiation) ,Condensed matter physics ,Inflection point ,Density of states ,Statistical and Nonlinear Physics ,Cooper pair ,Condensed Matter Physics ,Curvature ,Magnetic susceptibility ,Spin-½ ,Fermi Gamma-ray Space Telescope - Abstract
The magnetic susceptibility χ in La 2-x Sr x CuO 4 shows unusual concentration x- and temperature T-behaviors. The χ at 400 K increases with x in the range 0.040+B0/T. The Cooper pair (pairon) has no net spin, and hence its spin contribution to χ is zero. But its motion with the linear dispersion relation: ∊=(2/π)vFp, where vF=Fermi speed, can generate a T-dependent contribution -B1/T. These two contributions generate a χ-maximum at Tm in the range 0.15
- Published
- 2000
30. QUANTUM THEORY OF THE SEEBECK COEFFICIENT IN METALS
- Author
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Shigeji Fujita, Y. Okamura, and H. C. Ho
- Subjects
Brillouin zone ,Physics ,Condensed matter physics ,Einstein relation ,Seebeck coefficient ,Quantum mechanics ,Density of states ,Statistical and Nonlinear Physics ,Fermi surface ,Fermi energy ,Diffusion (business) ,Condensed Matter Physics ,Thermoelectric materials - Abstract
Based on the idea that different temperatures generate different carrier densities and the resulting diffusion causes the thermal emf, a new formula for the Seebeck coefficient S is obtained: [Formula: see text], where q, n, εF, [Formula: see text]. and [Formula: see text]. are respectively charge, carrier density, Fermi energy, density of states at ∊F and volume. Ohmic and Seebeck currents are fundamentally different in nature. This difference can cause significantly different transport behaviors. For a multi-carrier metal the Einstein relation between the conductivity and the diffusion coefficient does not hold in general. Seebeck (S) and Hall (RH) coefficients in noble metals have opposite signs. This is shown to arise from the Fermi surface having "necks" at the Brillouin boundary.
- Published
- 2000
31. KINETIC THEORY OF INFRARED HALL EFFECT IN SIMPLE METALS
- Author
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Yoshinobu Okamura, Young-Gi Kim, and Shigeji Fujita
- Subjects
Physics ,Condensed matter physics ,Hall effect ,Infrared ,Scattering ,Scattering rate ,Kinetic theory of gases ,Statistical and Nonlinear Physics ,Electron ,Conductivity ,Condensed Matter Physics ,Thermal conduction - Abstract
A kinetic theory is developed for the infrared (IR) Hall effect. The dynamic transport coefficients including the conductivity σ, cot θ H (θ H = Hall angle ) and the Hall coefficient R H for a system of conduction electrons ("electrons" or "holes") are shown to be obtained by applying the conversion rule: γ0 → γ(ω) -iω to the expressions for the static coefficients, where γ0 [γ(ω)] are static (dynamic) scattering rates which depend on the frequency ω and temperature T. If the real (Re) and imaginary (Im) parts of σ(ω) are measured, the ratio Re [σ(ω)]/ Im [σ(ω)] is equal to γ/ω, which directly gives the dynamic rate γ(ω, T). The ratio Re [ cot θ H ]/ Im [ cot θ H ] = -γ H (ω, T)/ω yields the dynamic Hall rate γ H (ω, T). The IR Hall effect experiments give a remarkable result: γ H (ω, T) = γ H , 0(T), that is, the dynamic Hall scattering rate is equal to the static rate up to mid-IR ~1000 cm -1.
- Published
- 2000
32. ON THE INFRARED HALL EFFECT ABOVE T<font>c</font> IN YBCO
- Author
-
Shigeji Fujita and Young-Gi Kim
- Subjects
Physics ,Drift velocity ,Condensed matter physics ,Infrared ,Hall effect ,Scattering ,Kinetic theory of gases ,Statistical and Nonlinear Physics ,Fermi energy ,Cooper pair ,Conductivity ,Condensed Matter Physics - Abstract
A kinetic theory is developed for the infrared Hall effect. Expressions for the dynamic conductivity σ(ω), ω = laser frequency, and other transport coefficients are shown to be obtained by applying the conversion rule: γ0 → γ -iω to those for the static coefficients, where γ0 (γ) are the static (dynamic) scattering rates. The observed T2-law of [Formula: see text] in YBa 2 Cu 3 O 7 are shown to arise from the drift velocity of the low-energy Cooper pairs (pairons) moving with the linear dispersion relation: ε = (2/π) v F p, where v F is the Fermi velocity.
- Published
- 2000
33. THEORY OF THE SEEBECK COEFFICIENT IN ALKALI AND NOBLE METALS
- Author
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Salvador Godoy, Shigeji Fujita, and Hung-Cheuk Ho
- Subjects
Physics ,Charge-carrier density ,Condensed matter physics ,Volume (thermodynamics) ,Seebeck coefficient ,Density of states ,Statistical and Nonlinear Physics ,Fermi surface ,Charge (physics) ,Fermi energy ,Condensed Matter Physics ,Alkali metal - Abstract
A new formula for the Seebeck coefficient S is obtained: [Formula: see text], where q, n, ε F , [Formula: see text] and [Formula: see text] are, respectively, charge, carrier density, Fermi energy, density of states at ε F and volume. Seebeck (S) and Hall (R H ) coefficients in alkali metals are both negative while these coefficients in noble metals have opposite signs. This difference is shown to arise from the different shapes of the Fermi surface.
- Published
- 1999
34. Formation of d-Wave Pairons in Cuprates via Longitudinal-Optical-Phonon Exchange
- Author
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Shigeji Fujita and David L. Morabito
- Subjects
Physics ,Condensed matter physics ,Phonon ,Condensed Matter::Superconductivity ,Condensed Matter::Strongly Correlated Electrons ,Statistical and Nonlinear Physics ,Cuprate ,Longitudinal optical ,Statistical physics ,Cooper pair ,Condensed Matter Physics ,Strong binding - Abstract
The d-wave Cooper pairs (pairons) in cuprates with a strong binding along the a- and b-axes are shown to arise from the optical-phonon-exchange attraction.
- Published
- 1998
35. Quantum Statistics of Cooper Pairs; Superconducting Temperature
- Author
-
David L. Morabito and Shigeji Fujita
- Subjects
Condensed Matter::Quantum Gases ,Momentum ,Superconductivity ,Physics ,Operator (computer programming) ,Quantum mechanics ,Statistical and Nonlinear Physics ,Fermi energy ,Fermion ,Cooper pair ,Condensed Matter Physics ,Quantum statistical mechanics ,Eigenvalues and eigenvectors - Abstract
We show that the eigenvalues of the number operator [Formula: see text] in the pair state (k1, k2), where c's and c†'s are fermion operators, are limited to 0 or 1, while the eigenvalues of the pair-number operator with the net momentum q≡ k1+k2 fixed, [Formula: see text], are 0, 1, 2,…. Both fermionic and bosonic natures of the Cooper pairs (pairons) must be used in the superconductivity theory. The Bose–Einstein condensation (BEC) of the pairons moving with a linear energy–momentum relation occurs at [Formula: see text] (3D), [Formula: see text] (2D), where n0 is the pairon density and v F the Fermi velocity. The connection between this [Formula: see text] and the BCS superconducting temperature is discussed.
- Published
- 1998
36. Quantum Statistics of Composites: Ehrenfest–Oppenheimer-Bethe's Rule
- Author
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David L. Morabito and Shigeji Fujita
- Subjects
Condensed Matter::Quantum Gases ,Physics ,High Energy Physics::Lattice ,Quantum dynamics ,Statistical and Nonlinear Physics ,Quantum capacity ,Fermion ,Condensed Matter Physics ,Open quantum system ,Quantum probability ,Quantum mechanics ,Quantum process ,Quantum gravity ,Quantum dissipation - Abstract
The quantum statistics of a composite is studied by looking at its Center-of-Mass (CM), which moves, following general principles of quantum theory and relativity. With respect to the CM motion the Ehrenfest–Oppenheimer–Bethe rule is shown to hold: a composite is fermionic if it contains an odd number of elementary fermions, bosonic if the number of fermions in it is even.
- Published
- 1998
37. Quantum Statistical Derivation of the Ginzburg–Landau Equation
- Author
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Shigeji Fujita and Salvador Godoy
- Subjects
Physics ,Equations of motion ,Statistical and Nonlinear Physics ,Condensed Matter Physics ,Kinetic energy ,symbols.namesake ,Nonlinear system ,symbols ,Cooper pair ,Penetration depth ,Hamiltonian (quantum mechanics) ,Wave function ,Quantum ,Mathematical physics - Abstract
The Cooper pair (pairon) field operator ψ†(r,t) changes, following Heisenberg's equation of motion. If the Hamiltonian ℋ contains pairon kinetic energies h0, a condensation energy α(1-r2), β>0, the evolution equation for ψ is nonlinear, from which we obtain the Ginzburg–Landau (GL) equation: [Formula: see text] for the GL wave function Ψσ(r)≡ 1/2|σ>, where σ denotes the state of the condensed pairons, and n the density operator. The GL equation with α=-εg(T) is shown to hold for all temperatures (T) below Tc, where εg is the pairon energy gap. Its equilibrium solution yields that the condensed pairon density n0(T)=|Ψσ(r)|2 is proportional to εg(T). The original GL T-dependence of the expansion parameters near Tc:α=-b(Tc-T), β= constant is justified. With the assumption of h0, a new formula for the penetration depth is obtained.
- Published
- 1998
38. [Untitled]
- Author
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E. S. Nam, Shigeji Fujita, D. Nguyen, and Salvador Godoy
- Subjects
Density matrix ,Physics ,Superconductivity ,Condensed matter physics ,Phonon ,Quantum mechanics ,Coulomb ,General Physics and Astronomy ,Cuprate ,Perturbation theory ,Cooper pair ,Quantum - Abstract
The electron-pair density matrix \gr(k 1, k 2; k 3, k 4, t) =: \gr(1, 2; 3, 4, t) changes in time, following a quantum Liouville equation with in the presence of a Coulomb interaction {itv}{in{itc}}, where \gW is the volume. If the virtual phonon exchange is in action, the density matrix \gr is shown to change similarly with an effective interaction {itv}{in{ite}}, by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.
- Published
- 1998
39. [Untitled]
- Author
-
Salvador Godoy and Shigeji Fujita
- Subjects
Physics ,symbols.namesake ,Quantum mechanics ,symbols ,General Physics and Astronomy ,Equations of motion ,Electron ,Cooper pair ,Kinetic energy ,Hamiltonian (quantum mechanics) ,Lambda ,Penetration depth ,Vector potential - Abstract
The Cooper pair (pairon) field operator ψ(r,t) changes in time, following Heisenberg’ s equation of motion. If the system Hamiltonian \(\mathcal{H}\) contains the pairon kinetic energies h0, the condensation energy per pairon α( 0, the evolution equation for ψ is non-linear, from which we obtain the Ginzburg-Landau equation: Open image in new window for the complex order parameter Ψσ(r) := | n1/2 | σ >, where σ denotes the state of the condensed pairons, and n the pairon density operator. The total kinetic energy h0 for “electron” (1) and “hole” (2) pairons is Open image in new window where vF(j) ≡ (2 eF / mj1/2 are Fermi velocities, and A the vector potential. A new expression for the penetration depth λ is obtained: $$\lambda = \frac{c} {e}\left[ {\frac{p} {{4\pi n_0 \left( {v_F^{(2)} + v_F^{(1)} } \right)}}} \right]^{1/2} ,$$ where p and n0 are respectively the momentum and density of condensed pairons.
- Published
- 1998
40. The Cooper pair dispersion relation
- Author
-
Antonio Puente, Montserrat Casas, Shigeji Fujita, A. Rigo, M. A. Solís, and M. de Llano
- Subjects
Superconductivity ,Physics ,Coupling ,Binding energy ,Energy Engineering and Power Technology ,BCS theory ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Momentum ,Orders of magnitude (time) ,Quantum mechanics ,Dispersion relation ,Electrical and Electronic Engineering ,Cooper pair - Abstract
The binding energy of a Cooper pair formed with the BCS model interaction potential is obtained numerically for all coupling in two and three dimensions for all non-zero center-of-mass momentum (CMM) of the pair. The pair breaks up for very small CMM, at most about four orders of magnitude smaller than the maximum CMM allowed by the BCS model interaction, and its binding energy is remarkably linear over the entire range of the CMM up to breakup.
- Published
- 1998
41. Means and Variances in Time Series Described by Unidirectional Random Walks
- Author
-
Hiroaki Hara, Sang Seok Lee, Mitsunobu Miyagi, and Shigeji Fujita
- Subjects
Path (topology) ,Physics ,Fractal ,Physics and Astronomy (miscellaneous) ,Integer ,Series (mathematics) ,Mathematical analysis ,Jump ,Exponent ,Random walk ,Constant (mathematics) - Abstract
An exactly solvable spatio-temporal model (time series) is proposed. The solution of this model is obtained as the most probable path determined by counting the number of all possible paths in the cells obtained by dividing a spatio-temporal space. The model is characterized by two parameters, a maximum jump distance pa (a = unit step and p = integer) and a fractal geometrical exponent v (ato = constant, to = unit time).
- Published
- 1997
42. Electrical Conduction in Graphene and Nanotubes
- Author
-
Akira Suzuki and Shigeji Fujita
- Subjects
Materials science ,Condensed matter physics ,Graphene ,law ,Electrical conduction ,Ballistic conduction in single-walled carbon nanotubes ,Bilayer graphene ,Graphene nanoribbons ,law.invention - Published
- 2013
43. Composite-particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect
- Author
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Akira Suzuki, Hung-Cheuk Ho, and Shigeji Fujita
- Subjects
Physics ,Condensed Matter::Quantum Gases ,Electron density ,Condensed Matter - Mesoscale and Nanoscale Physics ,Physics and Astronomy (miscellaneous) ,Condensed matter physics ,General Mathematics ,FOS: Physical sciences ,Charge (physics) ,02 engineering and technology ,Fermion ,Electron ,Quantum Hall effect ,021001 nanoscience & nanotechnology ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,01 natural sciences ,0103 physical sciences ,Fractional quantum Hall effect ,Composite fermion ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,010306 general physics ,0210 nano-technology ,Boson - Abstract
A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron ("electron", "hole") and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with \emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_\phi^{(m)}$, is connected with the electron density $n_{\mathrm e}$ by $n_\phi^{(m)}=n_{\mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $\sigma_{\mathrm H}\equiv j/E_{\mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_\phi^{(m)}$, is connected with the boson density $n_0$ by $n_\phi^{(m)}=n_0/m$. This yields $\sigma_{\mathrm H}=m\,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $\nu=1/m$ ($m=$odd numbers). Laughlin's theory and results about the fractional charge are not borrowed in the present work., Comment: 11 pages, 1 figure
- Published
- 2013
- Full Text
- View/download PDF
44. Bloch electron dynamics
- Author
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Shigeji Fujita, Salvador Godoy, and Diep Nguyen
- Subjects
Physics ,Particle in a one-dimensional lattice ,Condensed matter physics ,Hall effect ,Quantum electrodynamics ,Density of states ,General Physics and Astronomy ,Equations of motion ,Fermi surface ,Electron ,Curvature ,Bloch wave - Abstract
Newtonian equations of motion for the Bloch electron are derived and discussed in this chapter. “Electrons” (“holes”), which appear in the Hall coefficient mesurements, are generated near the Fermi surface on the negative (positive) curvature side of the surface.
- Published
- 1995
45. On the metal-insulator-transition in vanadium dioxide
- Author
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Shigeji Fujita, Salvador Godoy, Azita Jovaini, and Akira Suzuki
- Subjects
Physics ,Condensed Matter - Materials Science ,Condensed matter physics ,Wave packet ,Drop (liquid) ,General Physics and Astronomy ,Semiclassical physics ,Materials Science (cond-mat.mtrl-sci) ,FOS: Physical sciences ,Conductivity ,Thermal conduction ,Tetragonal crystal system ,Condensed Matter::Materials Science ,Condensed Matter::Strongly Correlated Electrons ,Metal–insulator transition ,Monoclinic crystal system - Abstract
Vanadium dioxide (VO$_2$) undergoes a metal-insulator transition (MIT) at 340 K with the structural change between tetragonal and monoclinic crystals as the temperature is lowered. The conductivity $\sigma$ drops at MIT by four orders of magnitude. The low-temperature monoclinic phase is known to have a lower ground-state energy. The existence of a $k$-vector ${\boldsymbol k}$ is prerequisite for the conduction since the ${\boldsymbol k}$ appears in the semiclassical equation of motion for the conduction electron (wave packet). Each wave packet is, by assumption, composed of the plane waves proceeding in the ${\boldsymbol k}$ direction perpendicular to the plane. The tetragonal (VO$_2$)$_3$ unit cells are periodic along the crystal's $x$-, $y$-, and z-axes, and hence there are three-dimensional $k$-vectors. The periodicity using the non-orthogonal bases does not legitimize the electron dynamics in solids. There are one-dimensional ${\boldsymbol k}$ along the c-axis for a monoclinic crystal. We believe this decrease in the dimensionality of the $k$-vectors is the cause of the conductivity drop. Triclinic and trigonal (rhombohedral) crystals have no $k$-vectors, and hence they must be insulators. The majority carriers in graphite are "electrons", which is shown by using an orthogonal unit cell for the hexagonal lattice., Comment: 8 pages, 1 figure
- Published
- 2012
46. Quantum Theory of Thermoelectric Power (Seebeck Coefficient)
- Author
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Akira Suzuki and Shigeji Fujita
- Subjects
Bass (sound) ,Materials science ,Thermoelectric generator ,Condensed matter physics ,Seebeck coefficient ,Thermoelectric effect ,Conductivity ,Thermoelectric materials ,Electron drift - Abstract
The conductivity σ is positive, but the Seebeck coefficient S can be positive or negative. We see that in Fig. 1, the measured Seebeck coefficient S in Al at high temperatures (400 – 670 ◦C) is negative, while the S in noble metals (Cu, Ag, Au) are positive (Rossiter & Bass, 1994). Based on the classical statistical idea that different temperatures generate different electron drift velocities, we obtain S = − cV 3ne , (1.4)
- Published
- 2011
47. Quantum statistical foundation to the fermi liquid model and Ginzburg-Landau wave function
- Author
-
Shigeji Fujita and Salvador Godoy
- Subjects
Physics ,Density matrix ,Physics and Astronomy (miscellaneous) ,Heisenberg model ,Quantum mechanics ,Operator (physics) ,Quantum oscillations ,Fermi surface ,Fermi liquid theory ,Condensed Matter Physics ,Fermi gas ,Wave function ,Electronic, Optical and Magnetic Materials - Abstract
An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in the k-space is given, starting with a realistic model of a metal including the Coulomb interaction among and between electrons and lattice-ions. The Ginzburg-Landau wave function [Psi][sub [sigma]](r), where [sigma] represents the superconducting pairon (Cooper-pair) state, is shown to be connected with the one-pairon density operator n by [Psi][sub [sigma]](r) = [l angle]r[vert bar]n[sup 1/2][vert bar][sigma][r angle]. A close analogy between supercurrent and laser is indicated. 31 refs.
- Published
- 1993
48. Relationship between superconductivity and band structures of electrons and phonons
- Author
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Seichi Watanabe and Shigeji Fujita
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Superconductivity ,Physics and Astronomy (miscellaneous) ,Condensed matter physics ,Phonon ,Electronic structure ,Electron ,BCS theory ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Electrical resistivity and conductivity ,Condensed Matter::Superconductivity ,Cooper pair ,Electronic band structure - Abstract
The relationship between superconductivity and band structures of electrons and phonons is established on the basis of a generalized Bardeen-Cooper-Schrieffer model in which the interaction strengths (V11,V12,V12) among and between “electron” (1) and “hole” (2) Cooper pairs are differentiated. Elemental superconductors must have local hyperboloidal Fermi surfaces called “necks” or “inverted double caps.”
- Published
- 1993
49. Superconductivity in Graphene and Nanotubes
- Author
-
Shigeji Fujita and Salvador Godoy
- Subjects
Superconductivity ,Materials science ,Graphene ,law ,Selective chemistry of single-walled nanotubes ,Nanotechnology ,Bilayer graphene ,Graphene nanoribbons ,law.invention - Published
- 2010
50. A quantum random‐walk model for tunneling diffusion in a 1D lattice. A quantum correction to Fick’s law
- Author
-
Shigeji Fujita and Salvador Godoy
- Subjects
Physics ,Particle in a one-dimensional lattice ,Wave packet ,Quantum mechanics ,Law ,Time evolution ,General Physics and Astronomy ,Quantum walk ,Scattering theory ,Physical and Theoretical Chemistry ,Random walk ,Fick's laws of diffusion ,Quantum tunnelling - Abstract
With the help of quantum‐scattering‐theory methods and the approximation of stationary phase, a one‐dimensional coherent random‐walk model which describes both tunneling and scattering above the potential diffusion of particles in a periodic one‐dimensional lattice is proposed. The walk describes for each lattice cell, the time evolution of modulating amplitudes of two opposite‐moving Gaussian wave packets as they are scattered by the potential barriers. Since we have a coherent process, interference contributions in the probabilities bring about strong departures from classical results. In the near‐equilibrium limit, Fick’s law and its associated Landauer diffusion coefficient are obtained as the incoherent contribution to the quantum current density along with a novel coherent contribution which depends on the lattice properties as [(1−R)/R]1/2.
- Published
- 1992
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