The minimal length of the differential segment in H-2 congenic lines

1982 ◽  
Vol 16 (4) ◽  
pp. 319-328 ◽  
Author(s):  
Dagmar Klein ◽  
Sneh Tewarson ◽  
Felipe Figueroa ◽  
Jan Klein
Keyword(s):  
Minimal Length ◽  
Differential Segment ◽  
Congenic Lines

Minimum space length

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Minimal Length ◽  
Space Length

We follow some logical principles to conclude there is a minimal length.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals Physics on the smallest scales: an introduction to minimal length phenomenology

2012 ◽  
Vol 33 (4) ◽  
pp. 853-862 ◽  
Author(s):  
Martin Sprenger ◽  
Piero Nicolini ◽  
Marcus Bleicher
Keyword(s):  
Minimal Length

DETERMINATION OF BREAKPOINT POSITIONS IN BARLEY TRANSLOCATIONS BY KARYOTYPE ANALYSIS OF PERMANENT RINGS OF SIX CHROMOSOMES

1974 ◽  
Vol 16 (3) ◽  
pp. 539-548 ◽  
Author(s):  
N. A. Tuleen ◽  
J. H. Gardenhire
Keyword(s):  
Karyotype Analysis ◽  
Chromosome 1 ◽  
Crossing Over ◽  
Differential Segment

Five T1-5 and 10 T1-6 barley translocations were crossed with the translocation T1-7f. Plants in which the T1-5 and T1-6 translocations had been combined with T1-7f due to crossing over in the differential segment were selected in the F2 generation. One of the chromosomes present in plants carrying the translocations in the combined form is made up of parts of the three chromosomes involved in the two translocations, and the segmental arrangement of this tripartite chromosome is determined by the position of the breakpoints in chromosome 1. The karyotypes of these stocks were analyzed and the breakpoints in seven of the translocations were assigned to the same arm and eight to the opposite arm of chromosome 1 relative to the position of the breakpoint in T1-7f.

Paths of Minimal Length Within Hypercubes

1966 ◽  
Vol 73 (8) ◽  
pp. 868 ◽  
Author(s):  
R. A. Jacobson
Keyword(s):  
Minimal Length

A geometric approach to quantum circuit lower bounds

2006 ◽  
Vol 6 (3) ◽  
pp. 213-262 ◽  
Author(s):  
M.A. Nielsen
Keyword(s):  
Lower Bounds ◽  
Geometric Approach ◽  
Quantum Circuit ◽  
Geodesic Equation ◽  
Initial Position ◽  
Minimal Length ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Minimal Size ◽  
Circuit Lower Bounds

What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on the manifold SU(2^n). The geodesic curves on these manifolds have the striking property that once an initial position and velocity are set, the remainder of the geodesic is completely determined by a second order differential equation known as the geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length geodesics provide lower bounds on quantum circuit size. For each Finsler metric we give a procedure to compute the corresponding geodesic equation. We also construct a large class of solutions to the geodesic equation, which we call \emph{Pauli geodesics}, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length geodesic is unique, it must be a Pauli geodesic; (b) finding the length of the minimal Pauli geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli geodesics of exponential length.

scholarly journals LAGRANGIAN FORMULATION OF A MAGNETOSTATIC FIELD IN THE PRESENCE OF A MINIMAL LENGTH SCALE BASED ON THE KEMPF ALGEBRA

2013 ◽  
Vol 28 (30) ◽  
pp. 1350142 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
B. KHOSROPOUR
Keyword(s):  
Integral Form ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Lagrangian Formulation ◽  
Length Scale ◽  
Magnetostatic Field ◽  
Classical Level ◽  
Spatial Dimensions ◽  
Minimal Length Scale ◽  
The Relationship

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β′)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length [Formula: see text]. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β′ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee–Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot–Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19m. The relationship between magnetostatics with a minimal length and the Gaete–Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

scholarly journals Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Tao ◽  
Peng Wang ◽  
Haitang Yang
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Statistical Physics ◽  
Turning Point ◽  
Minimal Length ◽  
Jacobi Method ◽  
Homogeneous Field ◽  
Quantization Rule ◽  
Connection Formula ◽  
Forbidden Region

In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up toOβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

Sign in / Sign up

Export Citation Format

Share Document