arXiv subjects

Daniel Dantchev

Publications and source records attributed to Daniel Dantchev.

At least 19 recordsLinked to original sources

arXiv2026

Casimir versus Helmholtz forces in the Gaussian model: exact results for Dirichlet--Dirichlet, Neumann--Dirichlet, Neumann--Neumann, and periodic boundary conditions

We present results and compare the behavior of two fluctuation-induced forces pertinent for their corresponding ensembles: the critical Casimir force in the grand canonical (fixed external field $h$) one and the critical Helmholtz force in the canonical (fixed average value of the order parameter $m$) one. We do so by deriving exact results for their behavior near the bulk critical point at $T=T_c$ in the three-dimensional Gaussian model. We consider Dirichlet-Dirichlet, Neumann-Dirichlet, Neumann-Neumann, and periodic boundary conditions. For every boundary condition examined, we confirm that both forces follow a finite-size scaling. We find that for Dirichlet-Dirichlet and Neumann-Dirichlet boundary conditions the Casimir and the Helmholtz force differ from each other. For Dirichlet-Dirichlet boundary conditions the Casimir force is always attractive, while the Helmholtz force can be both attractive and repulsive as a function of $T$ and $m$. For Neumann-Dirichlet boundary conditions the Casimir force changes sign from repulsive to attractive with increase of $h$, while the Helmholtz force stays always repulsive. Under periodic and Neumann-Neumann boundary conditions the Casimir force and the Helmholtz force coincide - the first does not depend on $h$, while the latter does not depend on $m$; they are always attractive.

cond-mat.stat-mech↗

arXiv2025

Casimir versus Helmholtz fluctuation induced force in { the Nagle}-Kardar model: Exact results

When used to describe \textit{finite} systems the {conjugate} statistical-mechanical ensembles are \textit{not} equivalent. This has physical implications for the behavior of the fluctuation induced forces pertinent to the different ensembles. Here, {we study the Nagle-Kardar model within the grand-canonical ensemble (GCE) and the canonical ensemble (CE) (with conserved total magnetization) for periodic boundary conditions (PBC)}. {We focus on two fluctuation-induce forces: the Casimir force (CF) in the GCE and the Helmholtz force (HF) in the CE}. In the infinite system limit the model exhibits a critical line, which ends at a tricritical point. Unexpectedly, the critical Casimir force (CCF) is \textit{repulsive} near the critical line and tricritical point, decaying rapidly upon departure from those two regions and becoming \textit{attractive}. This violates the widely-accepted ``boundary condition rule,'' which presumes that the CCF is attractive for equivalent boundary conditions (BC) and repulsive for conflicting BC. For the HF we find that it also changes sign as a function of temperature and the magnetization. We conclude, that CCF and HF have a behavior quite different from each other as a function of the tunable parameters (temperature, magnetic field, or magnetization) of the model. This dependence allows {for the control of the} \textit{sign} of these forces, as well as their magnitude.

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arXiv2024

Finite-size Nagle-Kardar model: Casimir force

We derive exact results for the critical Casimir force (CCF) within the Nagle-Kardar model with periodic boundary conditions (PBC's). The model represents one-dimensional Ising chain with long-range equivalent-neighbor ferromagnetic interactions of strength $J_{l}/N>0$ superimposed on the nearest-neighbor interactions of strength $J_{s}$ which could be either ferromagnetic ($J_{s}>0$) or antiferromagnetic ($J_{s}<0$). In the infinite system limit the model exhibits in the plane $(K_s=\beta J_s,K_l=\beta J_l)$ a critical line $2 K_l=\exp{\left(-2 K_s\right)}, K_s>-\ln3/4$, which ends at a tricritical point $(K_l=-\sqrt{3}/2, K_s=-\ln3/4)$. The critical Casimir amplitudes are: $\Delta_{\rm Cas}^{\rm (cr)}=1/4$ at the critical line, and $\Delta_{\rm Cas}^{\rm (tr)}=1/3$ at the tricritical point. Quite unexpectedly, with the imposed PBC's the CCF exhibits very unusual behavior as a function of temperature and magnetic field. It is \textit{repulsive} near the critical line and tricritical point, decaying rapidly with separation from those two singular regimes fast away from them and becoming \textit{attractive}, displaying in which the maximum amplitude of the attraction exceeds the maximum amplitude of repulsion. This represents a violation of the widely-accepted ``boundary condition rule,'' which holds that the CCF is attractive for equivalent BC's and repulsive for conflicting BC's \textit{independently} of the actual bulk universality class of the phase transition under investigation.

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arXiv2024

A Brief Survey of Fluctuation-induced Interactions in Micro- and Nano-systems and One Exactly Solvable Model as Example

Fluctuations exist in any material object $A$. If $A$ has non-zero temperature $T$, one speaks about thermal fluctuations. If $A$ is at very low $T$, the fluctuations are of quantum origin. Interesting effects appear if two bodies $A$ and $B$ are separated by a fluctuating medium $C$ (say a vacuum, or a fluid close to its {\it critical point}) when the fluctuations are long-ranged, i.e., they decay according to a power-law with the distance. Then the changes of fluctuations in $C$ due to the surfaces and constituents of $A$ are also felt by $B$, and \textit{vice versa}, which leads to a fluctuation induced force (FIF) between them. This force persists in addition to the direct influence of $A$ on $B$ (say, via gravity or Coulomb's force). These FIF's can be of attractive or repulsive character. They may play crucially important role on phenomena involving objects with length scale comparative with the Universe, as well as to the tiny objects relevant for MEMS and NEMS. In the current article we present some basic facts for the FIF and their diversity. Then on the example of one dimensional Ising model with a defect bond we present some new analytical results for such forces.

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arXiv2023

Fluctuation-induced Interactions in Micro- and Nano-systems: Survey of Some Basic Results

On the examples of the quantum-electrodynamical Casimir force, as well as critical Casimir and Helmholtz forces, we present a review of some results available for the class of fluctuation induced forces. In addition, we also concisely present examples of other such fluctuation-induced forces. On the instance of the Ising model we discuss the connection between the Casimir and Helmholtz forces. We discuss the importance of the presented results for the nanotechnology, and especially for devising micro- or nano-systems, and for their assembly. Some important problems for the nanotechnology, following from the currently available experimental findings, are spelled out and possible strategies for their overcoming are outlined.

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arXiv2022

Exact expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble

We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble, for three commonly-used boundary conditions: periodic, antiperiodic and Dirichlet. These expressions allow for the determination of fluctuation-induced forces in the canonical ensemble, which we term Helmholtz forces. The thermodynamic expressions and the calculations flowing from them should provide insights into the nature and behavior of fluctuation induced forces in interesting and as-yet unexplored regimes.

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arXiv2019

Behavior of the van der Waals force between a plate and a single-walled carbon nanotube under uniform hydrostatic pressure: a theoretical study

We study the behaviour of the non-retarded van der Waals force between a planar substrate and a single-walled carbon nanotube, assuming that the system is immersed in a liquid medium which exerts hydrostatic pressure on the tube's surface, thereby altering its cross-section profile. The shape of the latter is described as a continual structure characterized by its symmetry index $n$. Two principle mutual positions of the tube with respect to the substrate are studied: when one keeps constant the minimal separation between the surfaces of the interacting objects; when the distance from the tube's axis to the substrates bounding surface is fixed. Within these conditions, using the technique of the surface integration approach, we derive an integral form of the expressions which give the dependence of the commented force on the applied pressure.

cond-mat.mes-hall↗

arXiv2019

Exact results for the Casimir force of a three-dimensional model of relativistic Bose gas in a film geometry

Recently it has been suggested that relativistic Bose gas of some type can be playing role in issues like dark matter, dark energy, and in some cosmological problems. In the current article we investigate one known exactly solvable model of three-dimensional statistical-mechanical model of relativistic Bose gas that takes into account the existence of both particles and antiparticles. We derive exact expressions for the behavior of the Casimir force for the system subjected to film geometry under periodic boundary conditions. We show that the Casimir force between the plates is attractive, monotonic as a function of the temperature scaling variable, with a scaling function that approaches at low temperatures a universal negative constant equal to the corresponding one for two-component three dimensional Gaussian system. The force decays with the distance in a power law near and below the bulk critical temperature $T_c$ of the Bose condensate and exponentially above $T_c$. We obtain closed form exact expression for the Casimir amplitude $\Delta_{\rm Cas}^{\rm RBG} =-4\zeta(3)/(5\pi)$. We establish the precise correspondence of the scaling function of the free energy of the model with the scaling functions of two other well-known models of statistical mechanics - the spherical model and the imperfect Bose gas model.

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arXiv2019

Exact solution for the order parameter profiles and the Casimir force in $^4$He superfluid films in an effective field theory

We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg's $Ψ$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by $d=3$, $ν=2/3$ and $β=1/3$, where $d$ is the bulk spatial dimension and $ν$ and $β$ are the usual critical exponents. In addition, we revisit relevant experiments \cite{GC99} and \cite{GSGC2006} in terms of our findings. We find reasonably good agreement between our theoretical predictions and the experimental data. We demonstrate analytically that our calculated force is attractive. The position of the extremum is predicted to be at $x_{\rm min}=π$, with $x=(L/ξ_0)(T/T_λ-1)^{1/ν}$, which value effectively coincides with the experimental finding $x_{\rm min}=3.2\pm 0.18$. Here $L$ is the thickness of the film, $T_λ$ is the bulk critical temperature and $ξ_0$ is the correlation length amplitude of the system for temperature $T>T_λ$. The theoretically predicted position of the minimum does not depend on the one adjustable parameter, $M$, entering the theory.

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arXiv2018

Exact solution of Ginzburg's $Ψ$-theory for the Casimir force in $^4$He superfluid films

We present an analytical solution of the Ginzburg's $Ψ$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point, and we revisit the corresponding experiments in light of our findings. We find reasonably good agreement between the $Ψ$-theory predictions and the experimental data. Our calculated force is attractive, and the largest absolute value of the scaling function is $1.848$, while experiment yields $1.30$. The position of the extremum is predicted to be at $x=(L/ξ_0)(T/T_λ-1)^{1/ν}=π$, while experiment is consistent with $x=3.8$. Here $L$ is the thickness of the film, $T_λ$ is the bulk critical temperature and $ξ_0$ is the correlation length amplitude of the system for $T>T_λ$.

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arXiv2017

Casimir Force in a Model with Strongly Adsorbing Competing Walls: Analytical Results

We present both analytical and numerical results for the behaviour of the Casimir force in a Ginzburg-Landau type model of a film of a simple fluid or binary liquid mixture in which the confining surfaces are strongly adsorbing but preferring different phases of the simple fluid, or different components of the mixture. Under such boundary conditions an interface is formed between the competing phases inside the system which are forced to coexist. We investigate the force as a function of the temperature and in the presence of an external ordering field and determine the (temperature-field) relief map of the force. We prove the existence of a single global maximum of the force and find its position and value. We find the asymptotic behavior of the force when any of the scaling fields becomes large while the other one is negligible. Contrary to the case of symmetric boundary conditions we find, as expected, that the finite system does not possess a phase transition of its own for any finite values of the scaling variables corresponding to the temperature and the ordering field. We perform the study near the bulk critical temperature of the corresponding bulk system and find a perfect agreement with the finite-size scaling theory.

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arXiv2017

Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces

We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. We study the interplay between these forces, as well as the {\it total} force (TF) between a spherical colloid particle and a thick planar slab, and between two spherical colloid particles. We do that using general scaling arguments and mean-field type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance $L$ from each other, confining the fluctuating fluid medium characterized by its temperature $T$ and chemical potential $μ$. The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called $(+,+)$ boundary conditions. On the other hand, the core region of the slab and the particles, influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes $T$, $μ$ or $L$, in {\it sign change} of the Casimir force (CF) {\it and} the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding, trapping and fixing of microparts in nanotechnology. Data for specific substances in support of the experimental feasibility of the theoretically predicted behavior of the CF and TF have been also presented.

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arXiv2017

Manipulation and amplification of the Casimir force through surface fields using helicity

We present both exact and numerical results for the behavior of the Casimir force in $O(n)$ systems with a finite extension in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems the Casimir force in certain temperature ranges is of the order of $L^{-2}$, both above and below the critical temperature, $T_c$, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one dimensional $XY$ and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle and the three dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean field version of the three dimensional $O(2)$ model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite size scaling.

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arXiv2015

Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials

We study the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance $L$ from each other confining a non-polar simple fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture. The slabs influence the fluid by long-range competing dispersion potentials. Under such conditions one usually expects {\it attractive} Casimir force governed by universal scaling function to which the dispersion potentials provide only corrections to scaling. We demonstrate, however, that below a given $L<L_{\rm crit}$ the competition between the effects due to the coatings and the slabs can result in {\it sign change} of the Casimir force when one changes the temperature $T$, the chemical potential of the fluid $μ$, or $L$. The last implies that by choosing specific materials for the slabs, coatings and the fluid for $L \lesssim L_{\rm crit}$ one can realize {\it repulsive} Casimir force with {\it non-universal} behavior which, upon increasing $L$, gradually turns into an {\it attractive} one described by an {\it universal} scaling function for $L\gg L_{\rm crit}$. We presented arguments and relevant data for specific substances in support of the experimental feasibility of the predicted behavior of the force.

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arXiv2015

Reply to Comment on "Casimir force in the $O(n\to\infty)$ model with free boundary conditions"

The proceeding comment raises a few points concerning our paper Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014). In this reply we stress that while Refs. Diehl \textit{et al.} EPL {\bf 100}, 10004 (2012) and Phys. Rev. E. {\bf 89}, 062123 (2014) use three different models to study the the Casimir force for the $O(n \rightarrow \infty)$ model with free boundary conditions we study a single model over the entire range of temperatures, from above the bulk critical temperature, $T_c$, to absolute temperatures down to $T=0$. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the comment, we make no claim for the superiority of our model over any of those considered by Diehl \textit{et al}. We also present additional evidence supporting our conclusion in Dantchev \textit{et al.}, Phys. Rev. E. {\bf 89}, 042116 (2014) that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as $L$ grows and remains accurate for values of the ratio $T/T_c$ that become closer and closer to unity, while $T$ remains well outside of the critical region.

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arXiv2014

Casimir force in the O(n -> infinity) model with free boundary conditions

We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness $L$ subject to free boundary conditions and described by the $n\to\infty$ limit of the $O(n)$ model. These results extend over all temperatures, including the critical regime near the bulk critical temperature $T_c$, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone's modes contributions. The temperature behavior when the absolute temperature, $T$, is a finite distance below $T_c$, up to a logarithmic-in-$L$ proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble - but do not duplicate - the experimental curve behavior for the force obtained for $^4$He films.

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arXiv2011

Casimir force in the rotor model with twisted boundary conditions

We investigate the three dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $α$ where $0 \le α\le π$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film---and the Casimir force it generates---as a function of the temperature $T$, the angle $α$, and the thickness $L$ of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter $α$ and the temperature and that can be attractive or repulsive. In particular, by varying $α$ and/or $T$ one controls \underline{both} the sign \underline{and} the magnitude of the Casimir force in a reversible way. Furthermore, for the case $α=π$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.

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arXiv2009

Finite-size effects in presence of gravity: The behavior of the susceptibility in $^3He$ and $^4He$ films near the liquid-vapor critical point

We study critical point finite-size effects on the behavior of susceptibility of a film placed in the Earth's gravitational field. The fluid-fluid and substrate-fluid interactions are characterized by van der Waals-type power law tails, and the boundary conditions are consistent with bounding surfaces that strongly prefer the liquid phase of the system. Specific predictions are made with respect to the behavior of $^3$He and $^4$He films in the vicinity of their respective liquid-gas critical points. We find that for all film thicknesses of current experimental interest the combination of van der Waals interactions and gravity leads to substantial deviations from the behavior predicted by models in which all interatomic forces are very short ranged and gravity is absent. In the case of a completely short-ranged system exact mean-field analytical expressions are derived, within the continuum approach, for the behavior of both the local and the total susceptibilities.

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