scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2020 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Harmonic Oscillators ◽  
General Belief ◽  
Classical Physics ◽  
Cell Edge ◽  
Newtonian Dynamics ◽  
New Form

In crystal periodic structure prediction, a basic and general equation is needed to determine their period vectors (cell edge vectors), especially under arbitrary external stress. It was derived in Newtonian dynamics years ago, which can be combined with quantum physics by further modeling. Here a new and concise approach based on the principles of statistical physics was employed to derive it into a new form, then applicable to both classical physics and quantum physics by its own. The new form also turned out to be the specific explicit equilibrium condition and the equation of state for crystals under external stress and temperature. Contrary to a general belief, the new form also concluded that harmonic oscillators can cause crystal thermal expansion.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2020 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Equation Of State ◽  
General Equation ◽  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Classical Physics ◽  
Cell Edge ◽  
Newtonian Dynamics ◽  
New Form

In crystal periodic structure prediction, a basic and general equation is needed to determine their period vectors (cell edge vectors), especially under arbitrary external stress. It was derived in Newtonian dynamics years ago, which can be combined with quantum physics by further modeling. Here a new and concise approach based on the principles of statistical physics was employed to derive it into a new form, then applicable to both classical physics and quantum physics by its own. The new form also turned out to be the specific explicit equilibrium condition and the equation of state for crystals under external stress and temperature. This work was also compared with the elasticity theory.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2019 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Quantum Mechanics ◽  
Periodic Structure ◽  
General Equation ◽  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Classical Physics ◽  
Cell Edge ◽  
Newtonian Dynamics

In crystal periodic structure prediction, a general equation is needed to determine the period vectors (cell edge vectors), especially when crystals are under arbitrary external stress. It has been derived in Newtonian dynamics years ago, which can be combined with quantum mechanics by further modeling. Here we derived such an equation in statistical physics, applicable to both classical physics and quantum physics by itself.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2020 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Temperature Dependent ◽  
Classical Physics ◽  
Linear Elastic ◽  
Dependent Form ◽  
New Form ◽  
Elastic Crystals

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2020 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Temperature Dependent ◽  
Classical Physics ◽  
Linear Elastic ◽  
Dependent Form ◽  
New Form ◽  
Elastic Crystals

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the mechanical equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2020 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Temperature Dependent ◽  
Classical Physics ◽  
Linear Elastic ◽  
Dependent Form ◽  
New Form ◽  
Elastic Crystals

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2020 ◽  
Author(s):  
Gang Liu
Keyword(s):  
Structure Prediction ◽  
Statistical Physics ◽  
Quantum Physics ◽  
External Stress ◽  
Temperature Dependent ◽  
Classical Physics ◽  
Linear Elastic ◽  
Dependent Form ◽  
New Form ◽  
Elastic Crystals

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2019 ◽  
Author(s):  
Gang Liu
Keyword(s):  
General Equation ◽  
Statistical Physics ◽  
Continuous Media ◽  
External Pressure ◽  
External Stress ◽  
Cell Edge ◽  
Newtonian Dynamics ◽  
Work Done ◽  
Crystal Cells

A basic and general equation to determine their period vectors (cell edge vectors) is necessary in physics, especially when crystals are under external stress. It has been derived in Newtonian dynamics in these years. Since statistical physics should also generate such, here we derive it. By extending the normal way for crystals under external pressure, regarding crystal cells as being filled with continuous media, writing the work done by the external stress on the crystal explicitly, and deriving the forces on the surfaces of the cells by the external stress, we arrived at the equation for the period vectors, which is in principle the same as the above mentioned counterpart achieved in Newtonian dynamics. It should be applicable when crystals are under different pressures in different directions, like in piezoelectric and piezomagnetic phenomena.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2019 ◽  
Author(s):  
Gang Liu
Keyword(s):  
General Equation ◽  
Statistical Physics ◽  
Continuous Media ◽  
External Pressure ◽  
External Stress ◽  
Cell Edge ◽  
Newtonian Dynamics ◽  
Work Done ◽  
Crystal Cells ◽  
Special Case

A basic and general equation to determine period vectors (cell edge vectors) is necessary in physics, especially when crystals are under external stress. It has been derived in Newtonian dynamics. Since statistical physics should also generate such equation, we will provide a derivation. By extending the normal derivation for crystals under external pressure, regarding crystal cells as being filled with continuous media, formulating the work done by the external stress on the crystal explicitly, and deriving the forces on the surfaces of the cells by the external stress, we arrived at the equation for the period vectors, which is in principle the same as the above mentioned counterpart achieved in Newtonian dynamics. Everything also restores when the external stress reduces to the special case of external pressure. It should be applicable when crystals are under different pressures in different directions, like in piezoelectric and piezomagnetic phenomena.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Classical Physics ◽  
Core Set ◽  
The World ◽  
Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

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