### Abstract

Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

Original language | English |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Russian Physics Journal |

DOIs | |

Publication status | Accepted/In press - 12 Nov 2016 |

### Fingerprint

### Keywords

- apparatus of density matrix
- components of the complex dielectric constant (CDC)
- non-stationary density matrix
- nonequilibrium polarization density matrix
- one-dimensional multi-well crystal potential relief of rectangular shape in an external field
- quantum Liouville kinetic equation
- quantum mechanism of spontaneous polarization of a ferroelectric material

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*, 1-8. https://doi.org/10.1007/s11182-016-0865-x

**Quantum Effects at a Proton Relaxation at Low Temperatures.** / Kalytka, V. A.; Korovkin, M. V.

Research output: Contribution to journal › Article

*Russian Physics Journal*, pp. 1-8. https://doi.org/10.1007/s11182-016-0865-x

}

TY - JOUR

T1 - Quantum Effects at a Proton Relaxation at Low Temperatures

AU - Kalytka, V. A.

AU - Korovkin, M. V.

PY - 2016/11/12

Y1 - 2016/11/12

N2 - Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

AB - Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

KW - apparatus of density matrix

KW - components of the complex dielectric constant (CDC)

KW - non-stationary density matrix

KW - nonequilibrium polarization density matrix

KW - one-dimensional multi-well crystal potential relief of rectangular shape in an external field

KW - quantum Liouville kinetic equation

KW - quantum mechanism of spontaneous polarization of a ferroelectric material

UR - http://www.scopus.com/inward/record.url?scp=84994761618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994761618&partnerID=8YFLogxK

U2 - 10.1007/s11182-016-0865-x

DO - 10.1007/s11182-016-0865-x

M3 - Article

SP - 1

EP - 8

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

ER -