Recent and earlier research
discussed in representative
publications
1. Properties of condensed
matter and fundamental physical constants
Liquid viscosity is strongly system-dependent and also
depends on temperature and pressure. It is not possible
to calculate liquid viscosity in general form due to
strong interactions, the same problem that exists for
liquid thermodynamics (see below). It turns out that
liquid viscosity at its minimum is universal. We have
recently shown how fundamental physical constants
provide the lower bound of liquid viscosity. This
minimal viscosity is a new quantum property, featuring
the Planck constant.
Interestingly, EM Purcell noted that "the viscosities
have a big range but they stop at the same place" (Am.
J. Phys., 1977), adding that he does not understand
this. Our results provide the answer to this question.
We have similarly applied our ideas to relate another
property, the speed of sound in condensed matter phases
to fundamental physical constants. We have found that
fundamental constants give the upper bound to the speed
of sound in solids and liquids of about 36 km/s. The
ratio of this bound to the speed of light depends on two
important dimensionless constants, the fine structure
constant and the proton-to-electron mass ratio.
2. The phonon theory of liquid thermodynamics
One
of the triumphs of physics has been the theory of solid
state developed at the beginning of the last century.
This provided a fundamental understanding of the basic
properties of solid matter such as the ability to absorb
and transfer heat. Solid state theory was preceded by
the equally successful theory of gases. But when we turn
to the third main phase of matter, the liquid phase,
most textbooks remain silent about the most basic liquid
properties such as heat capacity. Paradoxical though it
may seem in this age of scientific and technological
advancement, we still do not understand the most basic
aspects of liquid behaviour. The combination of strong
interactions with large atomic rearrangements has proved
to be the ultimate obstacle to developing a theory of
liquids. This was famously summarized by some in Landau
school as the "no small parameter" problem.
Landau&Lifshitz repeatedly assert that liquid energy
and heat capacity can not be calculated in general form,
contrary to solids and gases (Statistical Physics,
Pergamon Press, 1969, par. 66 and par. 74). This has
become an accepted view. I have proposed that contrary
to this statement and view, liquid energy and heat
capacity can in fact be calculated and understood.
L&L argument
concerns the approach to liquids in which the
interaction energy is calculated in addition to the gas
kinetic energy, as an integral over interatomic
potentials and correlations functions. This general
approach formed the basis for previous theories of
liquids. Apart from the problem of being system-specific
as discussed by L&L, there are other important
disadvantages of this approach: (a) interatomic
potentials and correlations functions are not generally
available, consequently, apart from very simple and
exotic liquids such as those composed of noble elements,
it has not been possible to calculate liquid energy and
heat capacity; (b) calculations become difficult beyond
simple cases and approximations difficult to control;
(c) it is not easy to see how the results are consistent
with large experimental decrease of liquid heat capacity
over a wide temperature range. On the other hand, in my
solid-like phonon approach to liquids (a) the liquid
energy does not depend on system-specific interatomic
interactions and correlation functions but on viscosity
only, and liquid viscosity is readily available however
complex the liquid is in terms of structure and
interactions. Importantly, in the context of L&L
argument above, this result is more universal in a sense
that liquids that are very different in terms of
interatomic interactions and correlation functions can
have the same viscosity at some temperature, and
therefore the same energy in my approach; (b) the
resulting equations are simple: the energy of a harmonic
liquid is no more complicated than the energy of a
harmonic solid; (c) the equations show good agreement
with experimental results over a wide temperature range
with no fitting parameters.
"The most detailed
and rigorous test of the phonon theory of
thermodynamics" was undertaken (J Proctor, Physics of
Fluids, 2020). Proctor notes that (a) the theory is
falsifiable and (b) his test did not falsify it.
3. Field theory of liquids and dissipation effects
I have proposed a Lagrangian theory of liquid dynamics
involving two scalar fields. Dissipation was believed to
be hard to describe by a Lagrangian, however in my
theory the energy dissipated by one field is taken up by
the second field. The theory results in gapped momentum
states (GMS), the effect which we now realize extends
beyond liquids and into other areas such as plasma,
holographic models, relativistic hydrodynamics and so
on.
4. A new line on a phase
diagram of matter above the critical point: the
Frenkel line
According to current understanding, no differences can
be made between a gas and a liquid above the critical
point, an abrupt terminus of the liquid-gas coexisting
line. Recently, we have discovered that this is not the
case, and that the phase diagram of matter should be
modified. We have proposed that a new line ("Frenkel
line") exists on the phase diagram above the critical
point at arbitrarily high pressure and temperature, and
which separates two physically distinct states of
matter. Crossing the line corresponds to qualitative
changes of physical properties of the system. The
Frenkel line has been since experimentally confirmed in
supercritical Ne, CH4, CO2, N2,
C2H6 and H2O using
X-ray, neutron and Raman scattering.
5. The problem of glass transition
The problem of glass transition is considered
as one of the deepest and most interesting challenges in
physics. The problem consists of two parts, dynamic and
thermodynamic. The thermodynamic part of the problem of
glass transition is related to two widely observed
experimental facts: (a) heat capacity changes with a
jump at the glass transition temperature Tg, and (b) no
distinct solid glass phase has been identified
experimentally or suggested theoretically. Therefore,
the problem is to explain the jump of heat capacity
without asserting the existence of a distinct solid
glass phase. This problem is also common to other
disordered systems, including spin glasses. I have
proposed that if, as is the case, Tg is defined as the
temperature at which the liquid stops relaxing at the
experimental time scale, the jump of heat capacity at Tg
follows as a necessary consequence due to the change of
system's elastic, vibrational and thermal properties.
The resulting equations have no fitting parameters, and
compare well with experimental results. This theory
explains widely observed time-dependent effects of glass
transition, including logarithmic increase of Tg with
the quench rate, and identifies three distinct regimes
of relaxation.
The dynamic
part of the problem of glass transition is to explain
the physical origin of several famous relaxation laws
and dynamic effects that liquids show in the glass
transformation range: the Vogel-Fulcher-Tammann law,
stretched-exponential relaxation, dynamic crossovers
etc. These phenomena are universal and are seen in other
systems as well (e.g. spin glasses), yet their physical
origin is not understood. I have proposed a solution to
this problem based on elastic interactions in a liquid.
The solution is based on a non-trivial way in which
high-frequency elastic waves propagate in a liquid.
Crucially, the propagation range of these waves
increases with liquid viscosity. This is in contrast to
frequently discussed hydrodynamic waves, whose
propagation range decreases with viscosity.
6. Radiation damage
Radiation
damage is a large and important area in science and
technology, and has far-reaching consequences for
materials performance in a wide range of applications,
including immobilization of nuclear waste and future
fusion reactors. This performance crucially depends on
whether a material is amorphizable by radiation damage
or is able to recover back to crystal. The phenomenon of
resistance to amorphization by radiation damage remains
largely not understood from theoretical standpoint. I
elucidated the phenomenon of resistance to amorphization
by radiation damage using massive parallel molecular
dynamics simulations. This was supported by
quantum-mechanical calculations of electronic structure.
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