Yacov Kantor

Tel Aviv University

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Yacov Kantor has a total of 58 co-authors. Here are the top co-authors by number of shared publications:

Mehran Kardar
Department of Physics, Massachusetts Institute of Technology
31 shared publications
Mehran Kardar
Department of Physics Massachusetts Institute of Technology 02139 Cambridge Massachusetts USA
14 shared publications
Oded Farago
Ben Gurion University of the Negev
8 shared publications
David J. Bergman
School of Physics and Astronomy, Tel-Aviv University, 69978 Tel-Aviv, Israel and Science Laboratories, Exxon Research and Engineering Company, Annandale, New Jersey 08801
5 shared publications
David R. Nelson
Department of Physics Harvard University Cambridge, Massachusetts 02138
5 shared publications
Ralf Metzler
University of Potsdam
5 shared publications

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Cited by 2
- 8 August 2024
- Published by American Physical Society (APS) in Physical Review E
Critical exponents of correlated percolation of sites not visited by a random walk
by Raz Halifa Levi, Yacov Kantor
We consider a $d$ -dimensional correlated percolation problem of sites not visited by a random walk on a hypercubic lattice $L^{d}$ for $d = 3$ , 4, and 5. The length of the random walk is $N = u L^{d}$ . Close to the critical value $u = u_{c}$ , many geometrical properties of the problem can be described as powers (critical exponents) of $u_{c} - u$ , such as $β$ , which controls the strength of the spanning cluster, and $γ$ , which characterizes the behavior of the mean finite cluster size $S$ . We show that at $u_{c}$ the ratio between the mean mass of the largest cluster $M_{1}$ and the mass of the second largest cluster $M_{2}$ is independent of $L$ and can be used to find $u_{c}$ . We calculate $β$ from the $L$ dependence of $M_{1}$ and $M_{2}$ , and $γ$ from the finite size scaling of $S$ . The resulting exponent $β$ remains close to 1 in all dimensions. The exponent $γ$ decreases from $\approx 3.9$ in $d = 3$ to $\approx 1.9$ in $d = 4$ and $\approx 1.3$ in $d = 5$ towards $γ = 1$ expected in $d = 6$ , which is close to $γ = 4 / (d - 2)$ .
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- 8 August 2024
- Published by American Physical Society (APS) in Physical Review E
Critical exponents of correlated percolation of sites not visited by a random walk
by Raz Halifa Levi, Yacov Kantor
We consider a $d$ -dimensional correlated percolation problem of sites not visited by a random walk on a hypercubic lattice $L^{d}$ for $d = 3$ , 4, and 5. The length of the random walk is $N = u L^{d}$ . Close to the critical value $u = u_{c}$ , many geometrical properties of the problem can be described as powers (critical exponents) of $u_{c} - u$ , such as $β$ , which controls the strength of the spanning cluster, and $γ$ , which characterizes the behavior of the mean finite cluster size $S$ . We show that at $u_{c}$ the ratio between the mean mass of the largest cluster $M_{1}$ and the mass of the second largest cluster $M_{2}$ is independent of $L$ and can be used to find $u_{c}$ . We calculate $β$ from the $L$ dependence of $M_{1}$ and $M_{2}$ , and $γ$ from the finite size scaling of $S$ . The resulting exponent $β$ remains close to 1 in all dimensions. The exponent $γ$ decreases from $\approx 3.9$ in $d = 3$ to $\approx 1.9$ in $d = 4$ and $\approx 1.3$ in $d = 5$ towards $γ = 1$ expected in $d = 6$ , which is close to $γ = 4 / (d - 2)$ .
Cited by 2
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Cited by 5
- 1 May 2022
- Published by IOP Publishing in Journal of Physics Communications
Quantum particle in a spherical well confined by a cone
by Raz Halifa Levi, Yacov Kantor
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle 2θ ₀ emanating from the center of the sphere, with 0 < θ ₀ < π. This non-central potential can be solved by an extension of techniques used in spherically-symmetric problems. The angular parts of the eigenstates depend on azimuthal angle φ and polar angle θ as P λ m ( cos θ ) e im φ where P λ m is the associated Legendre function of integer order m and (usually noninteger) degree λ. There is an infinite discrete set of values λ = λ i m (i = 0, 1, 3, ...) that depend on m and θ ₀. Each λ i m has an infinite sequence of eigenenergies E n ( λ i m ) , with corresponding radial parts of eigenfunctions. In a spherical box the discrete energy spectrum is determined by the zeros of the spherical Bessel functions. For several θ ₀ we demonstrate the validity of Weyl’s continuous estimate  W for the exact number of states  up to energy E, and evaluate the fluctuations of  around  W . We examine the behavior of bound states in a well of finite depth U ₀, and find the critical value U _c(θ ₀) when all bound states disappear. The radial part of the zero energy eigenstate outside the well is 1/r ^λ+1, which is not square-integrable for λ ≤ 1/2. (0 < λ ≤ 1/2) can appear for θ ₀ > θ _c ≈ 0.726π and has no parallel in spherically-symmetric potentials. Bound states have spatial extent ξ which diverges as a (possibly λ-dependent) power law as U ₀ approaches the value where the eigenenergy of that state vanishes.
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- 1 May 2022
- Published by IOP Publishing in Journal of Physics Communications
Open Access
Quantum particle in a spherical well confined by a cone
by Raz Halifa Levi, Yacov Kantor
We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle 2θ ₀ emanating from the center of the sphere, with 0 < θ ₀ < π. This non-central potential can be solved by an extension of techniques used in spherically-symmetric problems. The angular parts of the eigenstates depend on azimuthal angle φ and polar angle θ as P λ m ( cos θ ) e im φ where P λ m is the associated Legendre function of integer order m and (usually noninteger) degree λ. There is an infinite discrete set of values λ = λ i m (i = 0, 1, 3, ...) that depend on m and θ ₀. Each λ i m has an infinite sequence of eigenenergies E n ( λ i m ) , with corresponding radial parts of eigenfunctions. In a spherical box the discrete energy spectrum is determined by the zeros of the spherical Bessel functions. For several θ ₀ we demonstrate the validity of Weyl’s continuous estimate  W for the exact number of states  up to energy E, and evaluate the fluctuations of  around  W . We examine the behavior of bound states in a well of finite depth U ₀, and find the critical value U _c(θ ₀) when all bound states disappear. The radial part of the zero energy eigenstate outside the well is 1/r ^λ+1, which is not square-integrable for λ ≤ 1/2. (0 < λ ≤ 1/2) can appear for θ ₀ > θ _c ≈ 0.726π and has no parallel in spherically-symmetric potentials. Bound states have spatial extent ξ which diverges as a (possibly λ-dependent) power law as U ₀ approaches the value where the eigenenergy of that state vanishes.
Cited by 5
Open Access
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- 23 March 2021
- Published by arXiv in arXiv
Percolation Perspective on Sites Not Visited by a Random Walk in Two Dimensions
by Amit Federbush, Yacov Kantor
We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical simulations. Unlike its higher-dimensional counterparts, this problem has no sharp percolation threshold and the spanning (percolation) probability is a smooth function monotonically decreasing with $u$. The clusters of vacant sites are not fractal but have fractal boundaries of dimension 4/3. The lattice size $L$ is the only large length scale in this problem. The typical mass (number of sites $s$) in the largest cluster is proportional to $L^2$, and the mean mass of the remaining (smaller) clusters is also proportional to $L^2$. The normalized (per site) density $n_s$ of clusters of size (mass) $s$ is proportional to $s^{-\tau}$, while the volume fraction $P_k$ occupied by the $k$th largest cluster scales as $k^{-q}$. We put forward a heuristic argument that $\tau=2$ and $q=1$. However, the numerically measured values are $\tau\approx1.83$ and $q\approx1.20$. We suggest that these are effective exponents that drift towards their asymptotic values with increasing $L$ as slowly as $1/\ln L$ approaches zero.
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- 23 March 2021
- Published by arXiv in arXiv
Open Access
Percolation Perspective on Sites Not Visited by a Random Walk in Two Dimensions
by Amit Federbush, Yacov Kantor
We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical simulations. Unlike its higher-dimensional counterparts, this problem has no sharp percolation threshold and the spanning (percolation) probability is a smooth function monotonically decreasing with $u$. The clusters of vacant sites are not fractal but have fractal boundaries of dimension 4/3. The lattice size $L$ is the only large length scale in this problem. The typical mass (number of sites $s$) in the largest cluster is proportional to $L^2$, and the mean mass of the remaining (smaller) clusters is also proportional to $L^2$. The normalized (per site) density $n_s$ of clusters of size (mass) $s$ is proportional to $s^{-\tau}$, while the volume fraction $P_k$ occupied by the $k$th largest cluster scales as $k^{-q}$. We put forward a heuristic argument that $\tau=2$ and $q=1$. However, the numerically measured values are $\tau\approx1.83$ and $q\approx1.20$. We suggest that these are effective exponents that drift towards their asymptotic values with increasing $L$ as slowly as $1/\ln L$ approaches zero.
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Cited by 9
- 22 March 2021
- Published by American Physical Society (APS) in Physical Review E
Percolation perspective on sites not visited by a random walk in two dimensions
by Amit Federbush, Yacov Kantor
We consider the percolation problem of sites on an $L \times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N = u L^{2}$ steps, i.e., are vacant. Most of the results are obtained from numerical simulations. Unlike its higher-dimensional counterparts, this problem has no sharp percolation threshold and the spanning (percolation) probability is a smooth function monotonically decreasing with $u$ . The clusters of vacant sites are not fractal but have fractal boundaries of dimension 4/3. The lattice size $L$ is the only large length scale in this problem. The typical mass (number of sites $s$ ) in the largest cluster is proportional to $L^{2}$ , and the mean mass of the remaining (smaller) clusters is also proportional to $L^{2}$ . The normalized (per site) density $n_{s}$ of clusters of size (mass) $s$ is proportional to $s^{- τ}$ , while the volume fraction $P_{k}$ occupied by the $k th$ largest cluster scales as $k^{- q}$ . We put forward a heuristic argument that $τ = 2$ and $q = 1$ . However, the numerically measured values are $τ \approx 1.83$ and $q \approx 1.20$ . We suggest that these are effective exponents that drift towards their asymptotic values with increasing $L$ as slowly as $1 / ln L$ approaches zero.
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- 22 March 2021
- Published by American Physical Society (APS) in Physical Review E
Percolation perspective on sites not visited by a random walk in two dimensions
by Amit Federbush, Yacov Kantor
We consider the percolation problem of sites on an $L \times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N = u L^{2}$ steps, i.e., are vacant. Most of the results are obtained from numerical simulations. Unlike its higher-dimensional counterparts, this problem has no sharp percolation threshold and the spanning (percolation) probability is a smooth function monotonically decreasing with $u$ . The clusters of vacant sites are not fractal but have fractal boundaries of dimension 4/3. The lattice size $L$ is the only large length scale in this problem. The typical mass (number of sites $s$ ) in the largest cluster is proportional to $L^{2}$ , and the mean mass of the remaining (smaller) clusters is also proportional to $L^{2}$ . The normalized (per site) density $n_{s}$ of clusters of size (mass) $s$ is proportional to $s^{- τ}$ , while the volume fraction $P_{k}$ occupied by the $k th$ largest cluster scales as $k^{- q}$ . We put forward a heuristic argument that $τ = 2$ and $q = 1$ . However, the numerically measured values are $τ \approx 1.83$ and $q \approx 1.20$ . We suggest that these are effective exponents that drift towards their asymptotic values with increasing $L$ as slowly as $1 / ln L$ approaches zero.
Cited by 9
Open Access
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- 20 August 2019
- Published by arXiv in arXiv
Percolation of sites not removed by a random walker in $d$ dimensions
by Yacov Kantor, Mehran Kardar
How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of $N=uL^d$ steps on a $d$-dimensional hypercubic lattice of size $L^d$ (with periodic boundaries). We systematically explore dependence of the probability $\Pi_d(L,u)$ of percolation (existence of a spanning cluster) of sites not removed by the RW on $L$ and $u$. The concentration of unvisited sites decays exponentially with increasing $u$, while the visited sites are highly correlated -- their correlations decaying with the distance $r$ as $1/r^{d-2}$ (in $d>2$). Upon increasing $L$, the percolation probability $\Pi_d(L,u)$ approaches a step function, jumping from 1 to 0 when $u$ crosses a percolation threshold $u_c$ that is close to 3 for all $3\le d\le6$. Within numerical accuracy, the correlation length associated with percolation diverges with exponents consistent with $\nu=2/(d-2)$. There is no percolation threshold at the lower critical dimension of $d=2$, with the percolation probability approaching a smooth function $\Pi_2(\infty,u)>0$.
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- 20 August 2019
- Published by arXiv in arXiv
Open Access
Percolation of sites not removed by a random walker in $d$ dimensions
by Yacov Kantor, Mehran Kardar
How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of $N=uL^d$ steps on a $d$-dimensional hypercubic lattice of size $L^d$ (with periodic boundaries). We systematically explore dependence of the probability $\Pi_d(L,u)$ of percolation (existence of a spanning cluster) of sites not removed by the RW on $L$ and $u$. The concentration of unvisited sites decays exponentially with increasing $u$, while the visited sites are highly correlated -- their correlations decaying with the distance $r$ as $1/r^{d-2}$ (in $d>2$). Upon increasing $L$, the percolation probability $\Pi_d(L,u)$ approaches a step function, jumping from 1 to 0 when $u$ crosses a percolation threshold $u_c$ that is close to 3 for all $3\le d\le6$. Within numerical accuracy, the correlation length associated with percolation diverges with exponents consistent with $\nu=2/(d-2)$. There is no percolation threshold at the lower critical dimension of $d=2$, with the percolation probability approaching a smooth function $\Pi_2(\infty,u)>0$.
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Cited by 11
- 20 August 2019
- Published by American Physical Society (APS) in Physical Review E
Percolation of sites not removed by a random walker in $d$ dimensions
by Yacov Kantor, Mehran Kardar
How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of $N = u L^{d}$ steps on a $d$ -dimensional hypercubic lattice of size $L^{d}$ (with periodic boundaries). We systematically explore dependence of the probability $Π_{d} (L, u)$ of percolation (existence of a spanning cluster) of sites not removed by the RW on $L$ and $u$ . The concentration of unvisited sites decays exponentially with increasing $u$ , while the visited sites are highly correlated—their correlations decaying with the distance $r$ as $1 / r^{d - 2}$ (in $d > 2$ ). On increasing $L$ , the percolation probability $Π_{d} (L, u)$ approaches a step function, jumping from 1 to 0 when $u$ crosses a percolation threshold $u_{c}$ that is close to 3 for all $3 \leq d \leq 6$ . Within numerical accuracy, the correlation length associated with percolation diverges with exponents consistent with $ν = 2 / (d - 2)$ . There is no percolation threshold at the lower critical dimension of $d = 2$ , with the percolation probability approaching a smooth function $Π_{2} (\infty, u) > 0$ .
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- 20 August 2019
- Published by American Physical Society (APS) in Physical Review E
Percolation of sites not removed by a random walker in $d$ dimensions
by Yacov Kantor, Mehran Kardar
How does removal of sites by a random walk lead to blockage of percolation? To study this problem of correlated site percolation, we consider a random walk (RW) of $N = u L^{d}$ steps on a $d$ -dimensional hypercubic lattice of size $L^{d}$ (with periodic boundaries). We systematically explore dependence of the probability $Π_{d} (L, u)$ of percolation (existence of a spanning cluster) of sites not removed by the RW on $L$ and $u$ . The concentration of unvisited sites decays exponentially with increasing $u$ , while the visited sites are highly correlated—their correlations decaying with the distance $r$ as $1 / r^{d - 2}$ (in $d > 2$ ). On increasing $L$ , the percolation probability $Π_{d} (L, u)$ approaches a step function, jumping from 1 to 0 when $u$ crosses a percolation threshold $u_{c}$ that is close to 3 for all $3 \leq d \leq 6$ . Within numerical accuracy, the correlation length associated with percolation diverges with exponents consistent with $ν = 2 / (d - 2)$ . There is no percolation threshold at the lower critical dimension of $d = 2$ , with the percolation probability approaching a smooth function $Π_{2} (\infty, u) > 0$ .
Cited by 11
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Cited by 3
- 8 August 2018
- Published by American Physical Society (APS) in Physical Review E
Localization of random walks to competing manifolds of distinct dimensions
by Raz Halifa Levi, Yacov Kantor, Mehran Kardar
We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we consider a RW near a rectangular wedge in two dimensions, where the (zero-dimensional) corner and the (one-dimensional) wall have competing localization properties. This model applies also (as cross section) to an ideal polymer attracted to the surface or edge of a rectangular wedge in three dimensions. More generally, we consider $(d - 1)$ - and $(d - 2)$ -dimensional manifolds in $d$ -dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multicritical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.
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- 8 August 2018
- Published by American Physical Society (APS) in Physical Review E
Open Access
Localization of random walks to competing manifolds of distinct dimensions
by Raz Halifa Levi, Yacov Kantor, Mehran Kardar
We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we consider a RW near a rectangular wedge in two dimensions, where the (zero-dimensional) corner and the (one-dimensional) wall have competing localization properties. This model applies also (as cross section) to an ideal polymer attracted to the surface or edge of a rectangular wedge in three dimensions. More generally, we consider $(d - 1)$ - and $(d - 2)$ -dimensional manifolds in $d$ -dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multicritical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two-dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.
Cited by 3
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Cited by 5
- 19 December 2017
- Published by American Physical Society (APS) in Physical Review E
Pinning and unbinding of ideal polymers from a wedge corner
by Raz Halifa Levi, Yacov Kantor, Mehran Kardar
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.
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- 19 December 2017
- Published by American Physical Society (APS) in Physical Review E
Open Access
Pinning and unbinding of ideal polymers from a wedge corner
by Raz Halifa Levi, Yacov Kantor, Mehran Kardar
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.
Cited by 5
Open Access
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- 25 August 2017
- Published by arXiv in arXiv
Attractive and repulsive polymer-mediated forces between scale-free surfaces
by Yacov Kantor, Mehran Kardar
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles, but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone), when the polymer is repelled by the obstacles, or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer mediated force equals ${\cal A} \, k_{B}T/h$, where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of ${\cal A}$, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e. at this special point there is no polymer-mediated force between obstacles (scale-free or not).
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- 25 August 2017
- Published by arXiv in arXiv
Open Access
Attractive and repulsive polymer-mediated forces between scale-free surfaces
by Yacov Kantor, Mehran Kardar
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles, but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone), when the polymer is repelled by the obstacles, or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer mediated force equals ${\cal A} \, k_{B}T/h$, where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of ${\cal A}$, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e. at this special point there is no polymer-mediated force between obstacles (scale-free or not).
Open Access
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Cited by 4
- 24 August 2017
- Published by American Physical Society (APS) in Physical Review E
Attractive and repulsive polymer-mediated forces between scale-free surfaces
by Yacov Kantor, Mehran Kardar
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals $A k_{B} T / h$ , where $T$ is temperature. The amplitude $A$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of $A$ , which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find $A = 0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).
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- 24 August 2017
- Published by American Physical Society (APS) in Physical Review E
Open Access
Attractive and repulsive polymer-mediated forces between scale-free surfaces
by Yacov Kantor, Mehran Kardar
We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation $h$ between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals $A k_{B} T / h$ , where $T$ is temperature. The amplitude $A$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of $A$ , which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find $A = 0$ for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).
Cited by 4

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