scholarly journals An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, the unitary group and the Pauli group

2009 ◽  
Vol 42 (35) ◽  
pp. 353001 ◽  
Author(s):  
Maurice R Kibler
Keyword(s):  
Fourier Transform ◽  
Angular Momentum ◽  
Unitary Group ◽  
Hadamard Matrices ◽  
Gauss Sums ◽  
Mutually Unbiased Bases

scholarly journals Real entries of complex Hadamard matrices and mutually unbiased bases in dimension six

2019 ◽  
pp. 1-18 ◽  
Author(s):  
Mengfan Liang ◽  
Mengyao Hu ◽  
Yize Sun ◽  
Lin Chen ◽  
Xiaoyu Chen
Keyword(s):  
Hadamard Matrices ◽  
Mutually Unbiased Bases

scholarly journals Angular momenta in fields from a rotational mechanical antenna

2021 ◽  
Author(s):  
Yu Mao ◽  
Y. Liu ◽  
Hai Lin
Keyword(s):  
Fourier Transform ◽  
Angular Momentum ◽  
Electric Dipole ◽  
Energy Flow ◽  
Flow Density ◽  
Spin Angular Momentum ◽  
Transform Method ◽  
Rotation Direction ◽  
Binding Force ◽  
Angular Momenta

Abstract Mechanic antennas provide opportunities for human portable, VLF communications, where a rotational dipole emits EM signals with angular momenta. In this paper we analytically derive the electromagnetic fields from a rotational electric dipole using Fourier transform method, and find that the radiated fields from the rotational electric dipole carries nonzero energy flow density in both orbital and spin angular momentum (AM) parts by AM flux tensors. Intuitively, a rotation of a dipole induces a longitudinal orbital angular momentum and a longitudinal spin angular momentum both circulating in the rotation direction. And the binding force for the rotational electric dipole is then shown to result mainly from the Coulomb fields. We believe that our work can provide novel communication designs for portable mechanic antennas.

MULTIPARTITE QUANTUM SYSTEMS: PHASES DO MATTER AFTER ALL

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1877-1884 ◽  
Author(s):  
LUIS L. SÁNCHEZ-SOTO ◽  
ANDREI B. KLIMOV ◽  
HUBERT de GUISE
Keyword(s):  
Fourier Transform ◽  
Quantum Systems ◽  
Mutually Unbiased Bases ◽  
Dimensional System ◽  
Finite Fourier Transform ◽  
Diagonal Operators ◽  
Physical Requirement ◽  
Commuting Operators ◽  
Finite Dimensional ◽  
Comprehensive Theory

A comprehensive theory of phase for finite-dimensional quantum systems is developed. The only physical requirement imposed is that phase is complementary to amplitude. This complementarity is implemented by resorting to the notion of mutually unbiased bases. For a d-dimensional system, where d is a power of a prime, we explicitly construct d + 1 classes of maximally commuting operators, each one consisting of d - 1 operators. One of this class consists of diagonal operators that represent amplitudes and, by the finite Fourier transform, operators in this class are mapped to off-diagonal operators that can be appropriately interpreted as phases. The relevant example of a system of qubits is examined in detail.

Measuring Orbital Angular Momentum Quantum States in High-Dimensional Mutually Unbiased Bases

2013 ◽  
Author(s):  
Daniel Giovannini ◽  
Jacqui Romero ◽  
Jonathan Leach ◽  
Angela Dudley ◽  
Andrew Forbes ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Quantum States ◽  
High Dimensional ◽  
Mutually Unbiased Bases

scholarly journals Some new series of Hadamard matrices

1989 ◽  
Vol 46 (3) ◽  
pp. 371-383 ◽  
Author(s):  
Mieko Yamada
Keyword(s):  
Prime Power ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Gauss Sums ◽  
Quaternion Type ◽  
Generalized Quaternion

AbstractThe purpose of this paper is to prove (1) if q ≡ 1 (mod 8) is a prime power and there exists a Hadamard matrix of order (q − 1)/2, then we can construct a Hadamard matrix of order 4q, (2) if q ≡ 5 (mod 8) is a prime power and there exists a skew-Hadamard matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2), (3) if q ≡ 1 (mod 8) is a prime power and there exists a symmetric C-matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2).We have 36, 36 and 8 new orders 4n for n ≤ 10000, of Hadamard matrices from the first, the second and third theorem respectively, which were known to the list of Geramita and Seberry. We prove these theorems by using an adaptation of generalized quaternion type array and relative Gauss sums.

Construction of angular momentum eigenstates in the unitary group formalism for many-electron atomic systems

1982 ◽  
Vol 60 (3) ◽  
pp. 357-360 ◽  
Author(s):  
M. Schlesinger ◽  
R. D. Kent ◽  
G. W. F. Drake
Keyword(s):  
Angular Momentum ◽  
Unitary Group ◽  
Group Approach ◽  
Direct Construction ◽  
Atomic Systems ◽  
Unitary Group Approach ◽  
Lowering Operator

Efficient methods for the direct construction of angular momentum eigenstates in the unitary group approach to the theory of complex spectra are presented. We use raising/lowering operator techniques which avoid the need for more lengthy recursive formalisms.

scholarly journals Fourier transform over finite field and identities between Gauss sums

2003 ◽  
Vol 9 (1) ◽  
pp. 63-100 ◽  
Author(s):  
D. Kazhdan ◽  
A. Polishchuk
Keyword(s):  
Fourier Transform ◽  
Finite Field ◽  
Gauss Sums
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