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Daniel B. Litvin

Publications and source records attributed to Daniel B. Litvin.

6 recordsLinked to original sources
arXiv2017

Spatio-temporal Symmetry - Point Groups with Time Translations

Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by three-dimensional point group symmetry operations in combination with time translation operations are discussed in this work. The derivation of these 'spatio-temporal' groups from conventional point groups and their irreducible representations is outlined, followed by a complete listing. The groups are presented in a template similar to space group operations, and are visualized using a modified version of conventional stereographic projections. Simple examples of physical processes that simultaneously exhibit symmetry in space and time are identified and used to illustrate the application of spatio-temporal groups.

cond-mat.mtrl-sci↗
arXiv2014

The affine and Euclidean normalizers of the subperiodic groups

The affine and Euclidean normalizers of the subperiodic groups, the Frieze groups, the rod groups, and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane group Euclidean normalizers have been considered.

cond-mat.mtrl-sci↗
arXiv2013

Spontaneous tensor properties for multiferroic phases

We have constructed dichromatic matrices of property coefficients for all 1601 Aizu species. This involves 122 non-magnetic Aizu species and extends the work to the 773 species of phase transitions from disordered magnetic prototypic (parent) phases and the 616 species from ordered magnetic prototypic phases. In addition to coefficients describing the non-magnetic effects we have included the coefficients of pyromagnetic, magnetoelectric, piezomagnetic effects, and magnetic susceptibility. All components of these property tensors are displayed in 13 by 13 matrices; non-zero components of the prototypic phase are given in black and the spontaneous coefficients, that are non-zero in the ferroic phase and zero in the prototypic phase, are given in red.

cond-mat.mtrl-sci↗
arXiv2013

Double Antisymmetry and the Rotation-Reversal Space Groups

Rotation-reversal symmetry was recently introduced to generalize the symmetry classification of rigid static rotations in crystals such as tilted octahedra in perovskite structures and tilted tetrahedral in silica structures. This operation has important implications for crystallographic group theory, namely that new symmetry groups are necessary to properly describe observations of rotation-reversal symmetry in crystals. When both rotation-reversal symmetry and time-reversal symmetry are considered in conjunction with space group symmetry, it is found that there are 17,803 types of symmetry, called double antisymmetry, which a crystal structure can exhibit. These symmetry groups have the potential to advance understanding of polyhedral rotations in crystals, the magnetic structure of crystals, and the coupling thereof. The full listing of the double antisymmetry space groups can be found in the supplemental materials of the present work and online at our website: http://sites.psu.edu/gopalan/research/symmetry/

cond-mat.mtrl-sci↗
arXiv2011

New Symmetries in Crystals and Handed Structures

For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and counterclockwise directions as a distinct symmetry operation, here we show that there are many more structural symmetries than are currently recognized in right- or left-handed handed helices, spirals, and in antidistorted structures composed equally of rotations of both handedness. For example, though a helix or spiral cannot possess conventional mirror or inversion symmetries, they can possess them in combination with the rotation reversal symmetry. Similarly, we show that many antidistorted perovskites possess twice the number of symmetry elements as conventionally identified. These new symmetries predict new forms for "roto" properties that relate to static rotations, such as rotoelectricity, piezorotation, and rotomagnetism. They also enable symmetry-based search for new phenomena, such as multiferroicity involving a coupling of spins, electric polarization and static rotations. This work is relevant to structure-property relationships in all material structures with static rotations such as minerals, polymers, proteins, and engineered structures.

cond-mat.mtrl-sci↗