Representations of canonical anticommutation relations with orthogonality condition

2013 ◽  
Vol 64 (9) ◽  
pp. 1440-1447
Author(s):  
R. Ya. Yakymiv
Keyword(s):  
Orthogonality Condition ◽  
Canonical Anticommutation Relations

Combined User and Antenna Selection in Massive MIMO Using Precoding Technique

2019 ◽  
Vol 9 (2) ◽  
pp. 214-223 ◽  
Author(s):  
Tasher Ali Sheikh ◽  
Joyatri Bora ◽  
Md. Anwar Hussain
Keyword(s):  
Massive Mimo ◽  
Antenna Selection ◽  
Orthogonality Condition ◽  
Channel Gain ◽  
User Selection ◽  
Selection Algorithm

Background and Objectives: We propose here joint semi-orthogonal user selection and antenna selection algorithm based on precoding scheme. Methods: The focus of this proposed algorithm is to increase the system sumrate and decrease the complexity. We select and schedule users from a large number of users based on semi-orthogonality condition among them. Here, we select only the maximum channel gain antennas to maximize the system sumrate. Subsequently, the user selection and antenna selection have been scheduled in an adequate manner in order to obtain maximum system sumrate. We calculate the system sumrate for two scenarios: firstly, by considering the interference and secondly without considering the interference. We achieve maximum system sumrate at MMSE and lowest at without precoding while considering the interference. However, when we do not consider the interference we obtain lowest sumrate at MMSE and maximum at without precoding. Results and Conclusion: Here, we apply the precoding scheme to increase the system sumrate and we obtain approximately 20% to 35% higher system sumrate compared to without precoding, when interference is considered. Thus, we achieve higher sumrate in our proposed algorithms compared to other existing work.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

scholarly journals The Underlying Order Induced by Orthogonality and the Quantum Speed Limit

2021 ◽  
Vol 3 (3) ◽  
pp. 376-388
Author(s):  
Francisco J. Sevilla ◽  
Andrea Valdés-Hernández ◽  
Alan J. Barrios
Keyword(s):  
Energy Spectrum ◽  
Energy Distribution ◽  
Finite Time ◽  
Complete Characterization ◽  
Comprehensive Analysis ◽  
Orthogonality Condition ◽  
Speed Limit ◽  
Physical Quantities

We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

ALPHA CLUSTERING AND CONDENSATION IN NUCLEI

2011 ◽  
Vol 20 (04) ◽  
pp. 874-879 ◽  
Author(s):  
Y. FUNAKI ◽  
T. YAMADA ◽  
H. HORIUCHI ◽  
G. RÖPKE ◽  
P. SCHUCK ◽  
...  
Keyword(s):  
Orthogonality Condition ◽  
Low Density ◽  
Breakup Threshold ◽  
Condition Model ◽  
Strong Enhancement ◽  
Alpha Clustering ◽  
Α Particles

Low density states near the 3α and 4α breakup threshold in 12 C and 16 O , respectively, are discussed in terms of the α-particle condensation. Calculations are performed in OCM (Orthogonality Condition Model) and THSR (Tohsaki-Horiuchi-Schuck-Röpke) approaches. The [Formula: see text] state in 12 C and the [Formula: see text] state in 16 O are shown to have dilute density structures and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

REDUNDANCY OF MOMENT CONDITIONS AND THE EFFICIENCY OF OLS IN SUR MODELS

2008 ◽  
Vol 24 (5) ◽  
pp. 1456-1460 ◽  
Author(s):  
Hailong Qian
Keyword(s):  
Least Squares ◽  
Asymptotic Efficiency ◽  
Generalized Method Of Moments ◽  
Sufficient Conditions ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
American Statistical Association ◽  
Orthogonality Condition ◽  
Moment Conditions ◽  
Necessary And Sufficient

In this note, based on the generalized method of moments (GMM) interpretation of the usual ordinary least squares (OLS) and feasible generalized least squares (FGLS) estimators of seemingly unrelated regressions (SUR) models, we show that the OLS estimator is asymptotically as efficient as the FGLS estimator if and only if the cross-equation orthogonality condition is redundant given the within-equation orthogonality condition. Using the condition for redundancy of moment conditions of Breusch, Qian, Schmidt, and Wyhowski (1999, Journal of Econometrics 99, 89–111), we then derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of SUR models. We also provide several useful sufficient conditions for the equal asymptotic efficiency of OLS and FGLS estimators that can be interpreted as various mixings of the two famous sufficient conditions of Zellner (1962, Journal of the American Statistical Association 57, 348–368).

An Extremum Result

1962 ◽  
Vol 14 ◽  
pp. 597-601 ◽  
Author(s):  
J. Kiefer
Keyword(s):  
Probability Measure ◽  
Compact Space ◽  
Ad Hoc ◽  
Continuous Functions ◽  
Orthogonality Condition ◽  
Technical Detail ◽  
Real Numbers ◽  
Discrete Probability ◽  
Linearly Independent ◽  
Image Position

The main object of this paper is to prove the following:Theorem. Let f1, … ,fk be linearly independent continuous functions on a compact space. Then for 1 ≤ s ≤ k there exist real numbers aij, 1 ≤ i ≤ s, 1 ≤ j ≤ k, with {aij, 1 ≤ i, j ≤ s} n-singular, and a discrete probability measure ε*on, such that(a) the functions gi = Σj=1kaijfj 1 ≤ i ≤ s, are orthonormal (ε*) to the fj for s < j ≤ k;(b)The result in the case s = k was first proved in (2). The result when s < k, which because of the orthogonality condition of (a) is more general than that when s = k, was proved in (1) under a restriction which will be discussed in § 3. The present proof does not require this ad hoc restriction, and is more direct in approach than the method of (2) (although involving as much technical detail as the latter in the case when the latter applies).

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