On the orthogonality condition for the excited states of stationary quantum systems

1968 ◽  
Vol 46 (1) ◽  
pp. 43-47 ◽  
Author(s):  
C. S. Sharma
Keyword(s):  
Perturbation Method ◽  
Excited States ◽  
Quantum Systems ◽  
The State ◽  
Orthogonality Condition ◽  
Perturbation Expansions ◽  
Eigenvalues And Eigenvectors ◽  
Stationary Quantum ◽  
Common Misunderstanding

A theorem establishing the correct orthogonality condition for the perturbation expansions of the state vectors for the excited states of stationary quantum systems is enunciated. A common misunderstanding on this subject is discussed and corrected. Implications of the theorem to the use of the variation perturbation method for calculating approximate eigenvalues and eigenvectors for excited states is discussed.

FRUSTRATED TRANSVERSE ISING MODELS: A CLASS OF FRUSTRATED QUANTUM SYSTEMS

1992 ◽  
Vol 06 (14) ◽  
pp. 2439-2469 ◽  
Author(s):  
P. SEN ◽  
B. K. CHAKRABARTI
Keyword(s):  
Excited States ◽  
Transverse Field ◽  
Ising Models ◽  
Quantum Systems ◽  
Nearest Neighbour ◽  
Competing Interactions ◽  
Annni Model ◽  
Kirkpatrick Model ◽  
Transverse Fields ◽  
Exact Diagonalisation

The analytical and numerical (Monte Carlo and exact diagonalisation) estimates of phase diagrams of frustrated Ising models in transverse fields are discussed here. Specifically we discuss the Sherrington–Kirkpatrick model in transverse field and the Axial Next-Nearest Neighbour Ising (ANNNI) model in transverse field. The effects of quantum fluctuations (induced by the transverse field) on the ground and excited states of such systems with competing interactions (frustration) are also discussed. The results are compared to those available for other frustrated quantum systems.

scholarly journals USE OF THE WHIRLIGIG PRINCIPLE FOR STABILIZING THE INITIAL STATES OF SOME CLASSIC AND QUANTUM SYSTEMS

2020 ◽  
pp. 78-81
Author(s):  
V.A. Buts
Keyword(s):  
Quantum System ◽  
Excited States ◽  
Quantum Systems ◽  
Nuclear Systems ◽  
Initial States

It is shown that the whirligig principle can be used for stabilization of the initial states of some classical and quantum systems. This feature of the whirligig principle is demonstrated by simple examples. The most important result of this work is the proof of the fact that the stabilization of the excited states of quantum systems can be realized by acting not on the quantum system itself, but by acting on the states into which the system must go. Potentially, this result can be used to stabilize excited nuclear systems.

Quantum Error Correction

2020 ◽  
Author(s):  
Todd A. Brun
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Single Photon ◽  
Error Correcting Code ◽  
Quantum Systems ◽  
Quantum Error Correction ◽  
The State ◽  
Quantum States ◽  
Quantum Code ◽  
Quantum Error

Quantum error correction is a set of methods to protect quantum information—that is, quantum states—from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Most work on quantum error correction has focused on systems of quantum bits, or qubits, which are two-level quantum systems. These can be physically realized by the states of a spin-1/2 particle, the polarization of a single photon, two distinguished levels of a trapped atom or ion, the current states of a microscopic superconducting loop, or many other physical systems. The most widely used codes are the stabilizer codes, which are closely related to classical linear codes. The code space is the joint +1 eigenspace of a set of commuting Pauli operators on n qubits, called stabilizer generators; the error syndrome is determined by measuring these operators, which allows errors to be diagnosed and corrected. A stabilizer code is characterized by three parameters [[n,k,d]], where n is the number of physical qubits, k is the number of encoded logical qubits, and d is the minimum distance of the code (the smallest number of simultaneous qubit errors that can transform one valid codeword into another). Every useful code has n>k; this physical redundancy is necessary to detect and correct errors without disturbing the logical state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design. Other approaches to error mitigation in quantum systems include decoherence-free subspaces, noiseless subsystems, and dynamical decoupling.

α-PARTICLE CONDENSED STATE IN 16O

2009 ◽  
Vol 18 (10) ◽  
pp. 2083-2087
Author(s):  
Y. FUNAKI ◽  
T. YAMADA ◽  
H. HORIUCHI ◽  
G. RÖPKE ◽  
P. SCHUCK ◽  
...  
Keyword(s):  
Excited State ◽  
Strong Evidence ◽  
The State ◽  
Orthogonality Condition ◽  
Condensed State ◽  
Density Structure ◽  
Large Component ◽  
Condition Model ◽  
Strong Enhancement ◽  
Α Particles

The α-particle condensed state in 16 O is investigated by the use of 4α OCM (Orthogonality Condition Model). Low-lying spectrum in experiment is well reproduced up to around the 4α threshold. Furthermore, the excited state obtained around the 4α threshold as the [Formula: see text] state is shown to have a dilute density structure and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. This is strong evidence that the state is regarded as the 4α condensed state. It also has a large component of [Formula: see text] configuration, which is another reliable evidence of the state to be of 4α condensate nature.

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